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# Tag Info

## Hot answers tagged dc.distributed-comp

17

The paper you mention is important for 2 reasons: It shows that there is no asynchronous deterministic consensus algorithm that tolerates even a single crash fault. Note that in the synchronous setting,there is a deterministic algorithm that terminates in $f+1$ rounds when $\le f$ processes crash. It introduces bivalence and univalence of configurations (*),...

14

The distributed time complexity of numerous graph problems is still an open question. In general, distributed graph algorithms is an area in which we would expect to have (at least asymptotically) matching upper and lower bounds for the distributed time complexity of graph problems. For example, for many optimisation problems tight bounds are known. However,...

10

I will answer this from the perspective of distributed graph algorithms (distributed algorithms that solve a graph problem related to the structure of the communication network). Here are some non-obvious reasons for designing deterministic distributed algorithms in this setting: Subroutines in randomised algorithms. On p. 12–13 of these slides, Elkin ...

10

Why can we assume that property CP held when acceptor a0 voted for v in round k? It seems that we are using mathematical induction, therefore, what are the basis, inductive hypothesis, and inductive steps? You're looking at an instance of strong induction. In simple induction you assume the property holds for $n=m$ and prove it holds for $n=m+1$. In strong ...

9

Is there a set of canonical distributed systems problems from which all the possible distributed system problems can be reduced to? I'm unaware of such a published list of problems. Keep in mind that there are many different (and somewhat incomparable) models in distributed computing, ranging from the "benign" synchronous (fault-free) model where nodes ...

9

There are many research areas both in the theory and practice of distributed databases. One of the main practical challenges is that of implementing efficient concurrency control mechanisms for distributed and geo-replicated databases. In order to execute transactions efficiently, such mechanisms can provide weaker guarantees than serialisability, which ...

8

What are the advantages of linearizability as a safety property? Are there some results based on this fact in the literature? Suppose that you've implemented a shared memory machine $M$ that only satisfies eventual linearization, defined as follows: in every run $\alpha$ of $M$, there exists some point in time $T_\alpha$, such that linearization holds from ...

8

The exact quotation seems to be: "Pluralism: There is no central arbiter of truth in the system." See: http://archive.org/stream/byte-magazine-1985-04/1985_04_BYTE_10-04_Artificial_Intelligence#page/n237/mode/2up (p. 239, 2nd bullet point.)

7

Open problems on "Distributed Algorithms for Minimum Spanning Trees (MST)": (listed in [1]) Concerning time complexity, Near time optimal algorithms and lower bounds appear in [2] and references herein. The optimal time complexity remains an open problem. Concerning message complexity, As far as message complexity, although the asymptotically tight ...

7

It shows that there are no fault-tolerant deterministic algorithm. Quite a strong theoretical result, which forces designers to deal differently with fault-tolerance, some of which are synchronization and randomization. Comment: In my opinion, synchronization is an additional assumption of the system that are hardly found in practical applications. For ...

6

Regarding your first question - safety properties are, in a way, the "easiest" properties to handle, with respect to problems such as model-checking and synthesis. The basic reason for this is that in the automata-theoretic approach to formal methods, reasoning about safety properties reduces to reasoning about finite traces, which is easier than the ...

6

After a failed polynomial-time quick attempt, here it is an idea to prove that it is NP-complete using a reduction from 3SAT. Given a 3SAT formula with $x_1,...,x_n$ variables and $C_1,...,C_m$ clauses, first build a variable assignment gadget like in the figure below (thanks to @Jukka for the clarifications, the graph drawing style, and the hint for the ...

5

One reason consensus problems are important is that they are very simple and they are kind of universal problems for distributed computing systems. If we can solve consensus in an async distributed system we can use it to linearize actions on shared objects and obtain linearizability for shared objects. For simplicity, how many problems can you think of ...

5

I'm not aware of a general rule to convert centralized bounds to the distributed setting. In the distributed setting, local computation is given for free but the difficulty lies in breaking the symmetry - a node needs to accumulate enough information about it's neighborhood to make a decision about being part of the output set, e.g. being in the MIS. (Taking ...

4

The thing you get wrong is "we know that linearizability can be achieved in the asynchronous message passing system, while tolerating a minority of process crashes." We don't know that, and in fact it is wrong. What the quote from the JACM95 paper shows is that single-writer multi-reader registers can be implemented using message passing. And only this ...

4

A simple approach to achieve reliability and fast lookup in a "well connected" network $G$ is to replicate each file $f$ on a set $V_f$ of $\Theta(\sqrt{n}\log n)$ nodes and use random walks to efficiently find members of $V_f$. When searching for a file $f$, we start $c\sqrt{n}\in \Theta(\sqrt{n})$ random walks of length $\tau$ from some particular node, ...

4

This is a possible reduction from 3-partition which is strongly NP-complete. Given a set $A = \{a_1,a_2,...,a_{3m}\}$ of $3m$ positibe integers, and a target sum $B$. The basic idea is simple: if we found a read sequence like $Rx1\; Rx2\; Rx1$, even if the last write of $x$ before the sequence was a $Wx2$, the first $Rx1$ forces to "use" another $Wx2$ to ...

4

see also (more recently) a slideshow "Unsolved Computer Science Problems in Distributed Computing" from 2012 by Notre Dame researcher Douglas Thain who leads their cooperative computing lab. it has more of an applied slant but the key questions listed inevitably lead to theoretical areas. The Kiloscale Problem: Any workflow with sufficient concurrency ...

4

The model studied in the following work should be a fairly close match with the model that you described (see in particular graph problems "without edge duplication"): Woodruff & Zhang: "When Distributed Computation is Communication Expensive" http://arxiv.org/abs/1304.4636 See also this work for closely related models: Klauck et al.: "Distributed ...

3

This is a non-answer, but it might help to understand the question (assuming that I understood it correctly). Here is a simple but slightly non-trivial example: Here: input = black graph output = on which blue line we place each node = when to schedule each job costs = orange numbers = number of predecessors with different labels Left = simple greedy ...

3

The idea is growing territories. That is, a candidate broadcast to neighbors that are $\alpha^i$ away in iterations. The trick is in the analysis! (so it s not really clear) -- by getting to know the worst case of candidates, and the number of messages they send + setting $\alpha$ to a certain constant - we get $O(n)$ The solution can be found in N. ...

3

You can find a formal model and proof of Paxos and Byzantine Paxos written by L. Lamport et al at http://research.microsoft.com/en-us/um/people/lamport/tla/byzpaxos.html. The model can be checked using the TLA+ toolbox. Notice that the author of the Paxos algorithm, the formal model above, and even the TLA+ modeling language is the same person:)

3

As already suggested above, process algebra or process calculus is the place to start. Quoting freely from the respective Wikipedia page, History In the first half of the 20th century, various formalisms were proposed to capture the informal concept of a computable function, with μ-recursive functions, Turing Machines and the lambda calculus ...

3

What are the big challenges of designing distributed data structures (even harder than those of concurrent data structures)? Some important challenges that practically all distributed data structures face, are handling dynamic changes, implementing a scalable design, and being fault-tolerant. This includes finding answers to questions such as: How can we ...

3

The arXiv paper "Non-Monotonic Snapshot Isolation" [1] proves several impossibility theorems demonstrating that SI (Snapshot Isolation) and GPR (Genuine Partial Replication) are incompatible. To this end, it first decomposes SI into four properties: Decomposition theorem: $SI = ACA \cap SCONS \cap MON \cap WCF$ where, $ACA$: avoiding cascading aborts;...

3

You might want to look at the work of Gadi Taubenfeld. Many of his papers deal with impacts of different progress conditions such as (generalized) wait-freedom or obstruction-freedom on the computability power of shared objects in distributed systems, which includes registers.

3

In general, the results are pretty strongly negative --- fairly strong assumptions are needed for something like this to work. As an extreme case, suppose that training and testing distributions have disjoint supports, so that the training sample can be nearly uninformative regarding the test performance. That having been said, there is a body of research ...

2

Short answer: yes. Long answer: Using process algebra as a witness to the claimed existential is certainly admissible, but the way the question is phrased might warrant are more direct answer. If TMs are used as mathematical model for sequential computation, we can surely come up with a concurrent version, and show that it is no more powerful than the good ...

2

Edit: The answer below was written assuming that the ring is synchronous. Note that if node ids are chosen from some countable set and you don't care about time complexity, the $\Omega(n\log n)$ messages lower bound for electing a leader in a synchronous ring does not apply. In that case, there's an $O(n)$ messages algorithm that solves your problem: First,...

2

For synchronizing from a master list to a slave list, it looks like a fellow named Michael Heyeck has a good, O(n) solution to this problem. Check out that blog post for an explanation and some code. Perhaps this is a good starting point to generalize to a two-way sync. Essentially, the solution tracks both the master and slave lists in a single pass, ...

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# If $n > 1$, there are no non-zero $*$-homomorphisms $M_n(\Bbb{C}) \to \Bbb{C}$

If $$n > 1$$, there are no non-zero $$*$$-homomorphisms $$M_n(\Bbb{C}) \to \Bbb{C}$$. A $$*$$-homomorphism is an algebra morphism $$\varphi: M_n(\Bbb{C}) \to \Bbb{C}$$ with $$\varphi(\overline{A}^T) = \overline{\varphi(A)}$$

I tried to show that every $$*$$-morphism must be zero: if $$\varphi$$ is such a $$*$$-morphism, then $$E_{ij}^2 = 0$$ for $$i \neq j$$ (here $$E_{ij}$$ is the matrix that is $$1$$ on position $$(ij)$$, $$0$$ elsewhere). Thus $$\varphi(E_{ij}) = 0$$ for $$i \neq j$$. Hence, $$\varphi(A) = \sum_i a_{ii} \varphi(E_{ii})$$ so if I can show that $$\varphi(E_{ii}) = 0$$ I will be done. Unfortunately, I can't see why this should be true. I did not yet fully use the fact that it is a $$*$$-morphism. The only thing I can see is that $$\varphi(A) \in \Bbb{R}$$ for all $$A$$ since $$\varphi(E_{ii})= \varphi(\overline{E_{ii}}^T) = \overline{\varphi(E_{ii}})$$. If $$\varphi$$ is non-zero, then there is $$A$$ with $$\varphi(A) \in \Bbb{R}\setminus \{0\}$$. But then $$\varphi(iA) = i\varphi(A) \notin \Bbb{R}$$, a contradiction. Thus $$\varphi=0$$. Is this correct?

• Yes, or just use the algebra homomorphism condition on $E_{ii}=E_{ij}E_{ji}$, $j\neq i$. – user10354138 Jul 29 at 8:13
• @user10354138 So we actually have that every algebra morphism $M_n(\Bbb{C}) \to \Bbb{C}$ is zero? We don't need that it preserves the $*$-operations? – user745578 Jul 29 at 8:21
• Why would you have $\phi(A)\in\mathbb{R}$? The diagonal entries are not necessarily real. The trace is a map that has all the properties you used, and is certainly not zero. – MaoWao Jul 29 at 8:39
• @user1551 That is true, but I wrote "all the properties you used", and the OP did not use the multiplicativity of $\phi$ for anything but $\phi(E_{ij})=0$ for $i\neq j$, which is also true for the trace. – MaoWao Jul 29 at 8:43
• @user1551 Once again, I know that the trace is not multiplicative. But the trace also has the property that $\phi(E_{ij})=0$ for $i\neq j$ and $\phi(E_{ii})\in \mathbb{R}$. These two facts are not sufficient to show that $\phi=0$, and that is what the OP tries to do. – MaoWao Jul 29 at 8:48

We can prove that when $$n\ge2$$ and $$\mathbb F$$ is a field, the only mapping $$\phi:M_n(\mathbb F)\to\mathbb F$$ that is additive and multiplicative is zero. (So, we don't need $$\phi$$ to be an algebra morphism, not to say a $$\ast$$-homomorphism over $$\mathbb C$$.)
For any $$A\in M_n(\mathbb F)$$, we have $$A=P_1DQ$$ for some nonsingular matrices $$P_1,Q$$ and some diagonal matrix $$D$$. Let $$P_2$$ be any permutation matrix with a zero diagonal. Then $$P_2^TD$$ has a zero diagonal too. It follows that $$A=(P_1P_2)(P_2^TD)Q$$ can be written as $$A=P(L+U)Q$$ where $$P,Q$$ are nonsingular, $$L$$ is strictly lower triangular and $$U$$ is strictly upper triangular.
Since $$L^n=0$$, we have $$\phi(L)^n=\phi(L^n)=0$$. Therefore $$\phi(L)=0$$ and similarly $$\phi(U)=0$$. Hence $$\phi(A)=\phi(P)\left(\phi(L)+\phi(U)\right)\phi(Q)=0$$.


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# [texhax] hyperref

mahi mahi2308 at rediffmail.com
Thu Sep 18 05:36:11 CEST 2008

HI

Thanks for the reply. The example what u have given is write only its working for me also, but this example (dvips) doesn't create a link in the pdf,only pdflatex creates the link.

I wanted to know if there's a method to compile pdflatex without disturbing the figures (figures are in pdf format), all the figure i am converting from eps to pdf for pdflatex purpose because it will not read .eps files and i don't want to use .jpg format. But the problem is when i compile tex file using pdflatex, inside the figures some characters are not displaying because in eps format Open Type Fonts fonts have been used, and pdflatex using type1 fonts and type1 have only 256 characters and that character will not come under 256.

Because of this problem i am creating a pdf with dvi+ps+pfd option and in hyperref packages i am giving option as a dvips.

On Wed, 17 Sep 2008 Martin Heller wrote :
>mahi skrev:
> > I am MikTeX user, i am creating a pdf using hyperref.sty with dvips
> > option, after converting to dvi + ps + pdf when i click that link in pdf
> > for(reference, figures etc.......) it is not going to the proper place
> > just its going to the particular page, but if i use same package with
> > pdftex option the links goes to the particular references or figure, how
> > can i fix this bug for dvips option.
>
>hyperref can detect if you compile with pdflatex directly to pdf
>or with latex to dvi. In the latter case hyperref assumes you use
>dvips + ps2pdf to get the pdf. You don't need to specify dvips by
>option.
>
> > I might not be very clear, but basically i want to convert a hyper
> > linked pdf using dvi + ps + pdf, and in pdf when i click to the
> > reference citation that should go to the particular number of reference
> > section not particular page e.g. In text [15] if i click this in pdf it
> > should go to the reference [15].
>
>\documentclass[a4paper]{article}
>\usepackage{lipsum}
>\usepackage{hyperref}
>\begin{document}
>\ref{sec:foo}
>\lipsum[1-20]
>\section{Foo}
>\label{sec:foo}
>\lipsum[1]
>\end{document}
>
>The above works with both pdflatex and latex->dvips->ps2pdf on my
>MiKTeX system. You must be doing something differently.
>
>_______________________________________________
>TeX FAQ: http://www.tex.ac.uk/faq
>Mailing list archives: http://tug.org/pipermail/texhax/


text:
Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2623

 Title: Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term Authors: Hassan, Taher S. Keywords: Interval OscillationSecond OrderNonlinear Differential Equations Issue Date: 2008 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 34, No 4, (2008), 715p-732p Abstract: It is the purpose of this paper to give oscillation criteria for the second order nonlinear differential equation with a damping term (a(t) y′(t))′ + p(t)y′(t) + q(t) |y(t)| α−1 y(t) = 0, t ≥ t0, where α ≥ 1, a ∈ C1([t0,∞);(0,∞)) and p,q ∈ C([t0,∞);R). Our results here are different, generalize and improve some known results for oscillation of second order nonlinear differential equations that are different from most known ones in the sencse they are based on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line and can be applied to extreme cases such as ∫t0∞ q(t) dt = − ∞. Our results are illustrated with an example. Description: 2000 Mathematics Subject Classification: 34C10, 34C15. URI: http://hdl.handle.net/10525/2623 ISSN: 1310-6600 Appears in Collections: Volume 34, Number 4

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Let's say we're using a SolarWorld 315 Watt module with an ISC rationg of 9. Note! - in the calculator above FLA is RLA + 25%. 4 Pole Three phase circuits with neutral. Transformer calculations will automatically populate selected fields based upon embedded formulas in the calculator. 73 X 415 X 25 = 18kW. To calculate the full load current, enter 1,200kVAR as rating and voltage as 12,470V in the three phase calculator above. 8 × 3A × 110V / 1000 = 0. 8 Amps, so i need a 50 Amp breaker. 3-phase AC Panel Load Calc. If i have a power of 11. 240 V divided by 1. 4 Fire Pumps, Voltage Drop (mandatory calculation) 6. Breaker size must be rated for a minimum of 125% of the full-load current of the motor it is protecting, rounded up to the next standard breaker size. Unfollow 3 phase breaker to stop getting updates on your eBay Feed. Home›Calculators› Electrical calculators Online electrical calculators for calculations of electricity and electronics. Note that some types of single-phase loads are routinely supplied by a 3-phase panel. Mohamed - The current is for each phase. I'm getting conflicting reports on. Standards Related to High-Voltage Circuit Breakers 9. The fusible solution provides an interrupting. The lines would be connected via current transformers, and the tripping would be by external high voltage circuit breakers. Figure 3 shows an example of overduty breakers. one melting alloy thermal unit. 9 2 (4…5 poles) 315 38 5. Good practice would be to use a 2-pole breaker on each load or a 3-phase breaker to isolate everything at once. In vacuum circuit breaker the contacts are housed in a vacuum bottle, in which the contact separation occurs. 6 Amps per phase 16. From my calculations there will be approximately 30 A on the primary and 3. I-Line circuit breaker panelboards are designed, manufactured, and tested to comply with the following standards: Service I-Line circuit breaker panelboards can be used on the following system voltages: • 120/240 VAC; 1-phase, 3-wire • 240 VAC; 1-phase, 2-wire • 240 VAC; 3-phase, 3-wire • 240 VAC Ground, B-phase; 3-phase, 3-wire. The OP does reference 430. • Similar Requirements in OSHA 1910. The power taken by a circuit (single or three phase) is measured in watts W (or kW). Moment of inertia is the measure of an object's resistance to changes in its rotation rate. 35 do not apply to panelboards 3-Phase, 3-wire 3-Phase, 3-wire 3-Phase, 4-wire 3-Phase, 3-wire 3-Phase, 3-wire. To restore service, the circuit breaker must be reset (closed) after correcting the cause of the overload or failure. The combined kVA of three single-phase regulators connected in grounded wye will always be equal to the three phase regulator kVA for the system. The required generator size will then be displayed at the bottom. Air-conditioning and refrigeration equipment that employs only a single hermetic refrigerant motor-compressor shall comply with Parts C and D of Article 440. 8 and the phase current is 3A and the RMS voltage supply is 110V? Answer: the power P is equal to power factor of 0. Westinghouse circuit breakers are available in countless different configurations, both reconditioned and new. Appropriate for a two-pole 20-amp breaker or a single-pole 30-amp breaker. Three-phase induction motor consists of a stator and a rotor, and there is no electrical connection between these two. It's fine to exceed this for short periods of time, but continuous current above this amount could cause enough heat to trip the breaker. 9 14 15 5-6/10 1. Furthermore, the calculations of currents are often needed to demonstrate that. In a future blog (related to Short circuit), we will go deep and explain every single aspect of calculating the short circuit currents in a single phase and three phase power system. This task is not as easy as you may think. 248 and 430. There is a limit to the load that a single phase can handle and typically that number is set to 7. This interval is measured between relays in serie s eithe r at the instantaneous setting of the load sid e feeder circuit breaker relay or the maximum short-circuit current, which can flow through both dev ices simultaneously, whichever is the lower value of current. The open transition breaker-based Automatic Transfer Switch (ATS) will provide fully functioning transfer in applications where a momentary loss of power is acceptable on retransfer from emergency to normal power supply. Load on the circuit is 1 kW. Inrush Current Calculator – Single and Three Phase About us Since 1994, Ametherm has provided the most reliable and effective inrush current limiting solutions available. SMA recommends having a licensed solar contractor or electrician determine the correct conductor and breaker size. In the first case, each inverter is attached to a single line of the three phase system. They can be combined with our NEMA and IEC motor starters, overload relays, and contactors. High voltage circuit breakers. Multiply the amperage by 0. Let's say we're using a SolarWorld 315 Watt module with an ISC rationg of 9. (80% of Breaker Max. Breaker size must be rated for a minimum of 125% of the full-load current of the motor it is protecting, rounded up to the next standard breaker size. NFPA's family of codes and standards that deal with electrical issues - including NFPA 70®, National Electrical Code® (NEC®), NFPA 70B, Recommended Practice for Electrical Equipment Maintenance, and NFPA 70E, Standard for Electrical Safety in the Workplace, reflect changing industry needs and evolving technologies, supported by research and development, and practical experience. The net rating of the bank is 400*3=1,200kVAR. The high interrupting capacity of the breaker carries a 65kA rating. • Install a maximum 2 Pole 20 Amp circuit breaker • Use a minimum 12 AWG wire size • Engage Cable required 208 VAC Three-Phase External Branch (Home Run) Wiring Maximum Distance to Maintain 1% V Drop for 208 VAC Three-Phase Microinverters per Branch AWG 3 6 9 12 15 18 21 24 Maximum One-Way Wire Length (in Feet) to Maintain 1% V DROP. Switched Capacitor Breakers. 1: Where the values for branch-circuit short-circuit and ground-fault protective devices determined by Table 430. The bypass circuit breaker is a conventional AC circuit breaker. Divide kW by the power factor to get the kVA. Element (Time-Delay) Fuses, Instantaneous Trip Circuit Breakers, and Inverse Time Circuit Breakers. Capacities available 60, 100, 150, 200 Amp. 9 2 (4…5 poles) 315 38 5. 3 Circuit Breaker No. I am trying to size a circuit breaker for a transformer. as long as your 2. Constructing a steady-state model system for fault calculation to be used in the fault calculation, importing the model system and the failure electrolysis as an initial solution, assigning generator model and constant bus voltage to consider generator characteristics, 3 In case of phase short circuit accident, set breaker time (CPT) of each. Calculate electrical power transformer kva, current amps, and voltage. My calculation was 11500/(1. k2 Phase-to-phase short circuit. Introduction to Short Circuit Current Calculations. According to NEC,the general requirement for overload sizing be set around 115% or 125% from full load ampere. 8 14 25 25 1 16 14 30 30 1. Individual capacitors are connected line-neutral. 8 × 3A × 110V / 1000 = 0. If it holds, the breaker is good. 3 Amp so use 35A. Wiring for an Old 30 Amp, 240 Volt Circuit Breaker. You can use this formula for any load, to choose MCB (Miniature circuit breaker), Fuses and Over Load Relay (OLR) calculation. Feeder circuits supplying subpanels are 240-volt and require a double-pole circuit breaker. I am trying to size a circuit breaker for a transformer. Method 1 Substation with a single transformer When the plant foresees installation of an. Example DOL starter calculation Let us calculate the contactor and overload rating for DOL starter of the following motor: 7. It assumes the motor gets to speed quickly (a few seconds at most), or has a starter to reduce current during starting if it is taking too long. You can use this formula for any load, to choose MCB (Miniature circuit breaker), Fuses and Over Load Relay (OLR) calculation. If it is necessary to operate an unbalanced load, the equations below can be used to calculate the circuit values for open three phase Delta or Wye circuits. Above calculator is very useful for single phase. Hi, i'm a little confused about the way to calculate the amp of the circuit breaker for a three-phase system. Figure 3 shows an example of overduty breakers. Operating Mechanism 5. The performances are upgraded to 10kA. single-phase operation, single-phase power can be safely used with larger 3-phase rated inverters, provided that care is taken to properly upsize and apply the inverter. My question; is the 41. Note: If you had a 3-phase transformer, the formula would be Iprimary = KVA x 1000/(Vprimary x 1. Download Now. Three phase A/C turbines are more efficient in transmission of power to the batteries when the three phase rectifier is located near the batteries, so we will address 3 phase in a separate section. Conductor Size: Motor branch-circuit short-circuit and ground-fault protection (percentage of FLA from Tables 430. The size of your house's electrical service determines how many appliances you can run at one time. When placing multiple heaters on a circuit do not exceed the wattage listed for the corresponding wire and circuit breaker size. For calculation […]. If the breaker trips, the breaker is defective. I'm getting conflicting reports on. A "continuous load" is one where the maximum current is expected to continue for three hours or more. The maximum number of circles possible within a rectangle - ex. (In) = is the Circuit Breaker rating in Amps. General Electric Circuit Breaker Schematic Diagram. 3 and NEC 240. Voltage Drop Calculator Calculate the Conductor Size Based On The Project PLEASE NOTE: This Calculator will determine the minimum size conductor needed based on a 3% Voltage Drop. Element (Time-Delay) Fuses, Instantaneous Trip Circuit Breakers, and Inverse Time Circuit Breakers. …three-phase voltage downstream of Load Center No. Three-phase electric power is a common method of alternating current electric power generation, transmission, and distribution. According to your logic, a 3 phase 30a breaker will only carry 17. Calculate electrical power transformer kva, current amps, and voltage. 3-phase AC Panel Load Calc. Re: How to calculate load on 208v circuit versus a 120v circuit Pretty sure you need to multiply the 208 value by 1. 7 and round up to the next trade size of 15A. Amps to kW calculator;. Here's how it works, for single or three phase cable calculations, simply Input: The Load current, Length of cable run and Voltage drop i. The reader is encouraged to review AN109, References 3, 4, and 5 as background for this Application Note. Total FLA Calculation (Amp) 10. nema enclosed starter class 8536. The Three-Phase Breaker block uses three Breaker blocks connected between the inputs and the outputs of the block. Step 1 Three Phase - Find the FLC (full load current) - Table 430-150 three phase Step 2 Branch Circuit Conductor Sizing - 430-22 Single Motor: Calculate 125% of FLC = Ampacity - Turn to 310-16 to find the wire size. 15 when starting current is not a problem. They are both supplied from a 415V 3-ph system. Circuit breakers are rated in amperes at a specific ambient temperature. 75%6 = 11 Amp. All your cables, for all your projects. 3 - CIRCUIT BREAKER: a device designed to open and close a circuit by non- automatic means, and to open the circuit automatically on a predetermined overcurrent, without damage to itself when properly applied within its rating. Parameters. Circuit size Talk to your electrician and get the largest service you can afford for the sub-panel in your shop. If the cord and plug from the welder is rated at 50A, then the receptacle will have to have a minimum of 50A rating. He was a Journeyman Electrician, Master Electrician, and Electrical Contractor. 3 Transformer Circuit Fuses (N. Calculations are dictated by the national standard for Heating & Cooling. Calculation size of circuit breaker and fuse are as per NEC 450. I have two quotes from electricians for a supply to my summerhouse, 33 metres from my main consumer unit. Calculate Size of each Part of DOL starter for The System Voltage 415V,5HP Three Phase House hold Application Induction Motor,Code A, Motor efficiency 80%,Motor RPM 750,Power Factor 0. Short Circuit Current Calculations Three-Phase Short Circuits Basic Point-to-Point Calculation Procedure Step 1. The process used to size protective devices and circuit components is similar to the process used with other types of motor-operated equipment. The test sequence for I cn is "O - t - CO" where "O" is an open operation and "CO" is a close-open operation, which means that the circuit breaker under test is switched on and experiences the short-circuit current for a certain duration. 2 Pole Connection to active and neutral conductor OR Connection to two active conductors if device is suitably rated. 8-gauge or 6-gauge wire Used for 40-, 50- and 60-amp two-pole breakers; large appliances. They can be combined with our NEMA and IEC motor starters, overload relays, and contactors. Type - Circuit Breaker Loadcenter Breaker Mounting - Plug-On Phase - 3 Phase 4W Rating - Volts - 208Y/120-240V AC Mains - Breaker Main Breaker - CC 10kA IC Rating - Amps - 200 Number of Circuits - 42 Number of Spaces - (42) 1 in Enclosure - Indoor Cover - Surface/Flush Main Wire - Cu/Al 1-250mcm Manufacturer Series _ BR Length-47" Width-16. It has been some time but here goes. Let's say we're using a SolarWorld 315 Watt module with an ISC rationg of 9. RLA - "Running Load Amps" - current drawn during normal operation of electric motor. Molded case circuit breakers are a type of electrical protection device that is generally used for a wide range of voltages, and frequencies of both 50 Hz and 60 Hz. fractional hp n1 starter class 2510. distance about 110feet. Calculations must be conducted with both the maximum and minimum available three-phase (3Ø) bolted short-circuit current. My question; is the 41. calculate the capacity of capacitor panel if line power factor is. NEMA Contactor and Starter Specifications AC Coil Data Auxiliary Contacts (NEMA A600 and P300) — Bulletin 595, 596 NEMA Size Operating Volt Amperes Burden [VA] Heat Dissipation [W] Coil Operating Limits 60 Hz Coils Inrush Sealed 00 70 8 2. Unfollow 3 phase breaker to stop getting updates on your eBay Feed. Buck Boost Electronic Calculator, Calculates proper Square D Transformers to use when doing small changes in voltage: 5%, 6. 1) For three phase motor. 1 A; I'm wondering how three-phase breakers work. The circuit breaker is designed to break the circuit, cutting the power to the motor if the circuit starts pulling too much current. A Comparison of Circuit Breakers and Fuses for Low-Voltage Applications Tony Parsons, PhD, P. Asper nec code art430 First go to nec430. with 6 Elements, 3,333 Wafts each that are designed as two 10 KW, star-wired sets. 35 do not apply to panelboards 3-Phase, 3-wire 3-Phase, 3-wire 3-Phase, 4-wire 3-Phase, 3-wire 3-Phase, 3-wire. The dryer cable should have four wires, including the dedicated ground wire. The Three-Phase V-I Measurement block is used to measure instantaneous three-phase voltages and currents in a circuit. The wiring of both is same. 6 14 15 7 2 4. Your single phase breaker however can be a 100 amp because your peak 3-phase current is about 50amps times 1. How To Calculate The Cable Size Of A Motor By Using Kw Quora 3 10 three phase feeder size schedule engineering360 electrical cable wire sizing engineering centre square d overload size chart batan vtngcf org further electrical dimensional parameters for panel boards. Sizing the Circuit Breakers rev. In other words, the breaker controlling a circuit should be 125 percent of the continuous load (maximum current expected to last for three hours or more) and 100 percent of the non-continuous load. The circuit breakers in Class 8539 combination starters can be furnished with a factory installed auxiliary switch for remote indication of an open/tripped or closed circuit breaker. These breakers provide protection of circuits against overload, short circuit, and ground fault. 100, accessories: auxiliary contact, voltage release. 5kV Figure 3 Figure 4 Combined MV Circuit Breaker & Grounding Switch 0. Loadcenters & Circuit Breakers 3-47 3 Type BR Loadcenters & Circuit Breakers Loadcenter Product Selection Single-Phase — Main Circuit Breaker Loadcenters 10,000/25,000 Amperes Interrupting Capacity Table 3-70. First, determine the motor full-load current using Table 430. 8 and the phase current is 3A and the RMS voltage supply is 110V? Answer: the power P is equal to power factor of 0. HI, I am doing a research paper and I am trying to determine how to size a main circuit breaker for an MCC that supplies a number of three phase motors ranging from 0. The next higher standard-size circuit breaker is 20 amperes. 2(A)(1) for feeder conductors and 215. ) FLA=\frac{S_1\phi}{V_{line}} Figure 1: Calculation of short circuit rating of a single phase breaker. To begin, you need to know the wattage draw of your appliance(s) and make sure your generator produces enough power to handle that draw - lets' do it;. The Three-Phase Breaker block uses three Breaker blocks connected between the inputs and the outputs of the block. Description. Step 3 Branch Circuit Overcurrent Protection Sizing - 430-152 Select type of motor and type of over current protection device. According to your logic, a 3 phase 30a breaker will only carry 17. Home / Technical Articles / Sizing The DOL Motor Starter Parts (Contactor, Fuse, Circuit Breaker and Thermal Overload Relay) Calculate size of each part of DOL motor starter for the system voltage 415V, 5HP three phase house hold application induction motor, code A, motor efficiency 80%, motor RPM 750, power factor 0. The figure we would plug into the calculator would be: (40 x 1. Three pumps of a pump station (30, 10, and 1 ½ horsepower) are connected to the power source of 460-volts, 3-phase. We provide Pushmatic circuit breaker identification photographs including of electrical panels and of individual circuit breakers. Enter the rated volts, amps, power, and efficiency to find the current flowing through the motor. There are two general cases for this calculation. There are many factors to consider before choosing the proper gauge. How am I going to size my 3 phase X'mer with 1 phase load using current as reference [ 3 Answers ] Hi, I'm Peping: I have 90 pieces of single phase loads with current of 2 Amperes. The breaker will carry in the ambient temperature where it was calibrated. Sizing a Circuit Breaker. 73 in your calculation, because 120 is single phase where 208V should be Line to Line. How do I calculate right circuit breaker for any motor if I have three phase? Three phase doesn’t count for much. 2 for Copper Cable, Specific Resistance = 17. numbers of pipes or wires in a conduit. The circuit breaker is an absolutely essential device in the modern world, and one of the most important safety mechanisms in your home. Conduit sizes may need to be increased if equipment grounding conductors or neutrals are also installed in the conduit. 6 C4 Cable conductor size: Single-phase (230v) Circuit Am per %Vd. Choose your required voltage drop 3. These rating are adequate for runs of up to appx 60 ft. Wire Size Awg No. Calculate Size of each Part of DOL starter for The System Voltage 415V,5HP Three Phase House hold Application Induction Motor,Code A, Motor efficiency 80%,Motor RPM 750,Power Factor 0. Operating Mechanism 5. 8 and overload relay of. 1 is applicable to inverse time circuit breakers used for motor branch circuit, short-circuit, and ground-fault protection. 3%, 20%, and 26. Other models accept a wide range of fuse types, including Siemens exclusive three-pole circuit breaker shall be considered three over current devices. 8 Conduit Size if different size wires are used. Westinghouse circuit breakers are available in countless different configurations, both reconditioned and new. 240 x 25 x 3 = 18 kW. These rating are adequate for runs of up to appx 60 ft. I calculate this to be about 64 maximum amps. Cable Sizing Software - select, size and manage your power cables using myCableEngineering. Square D® is a global brand of Schneider Electric for NEMA-type electrical distribution and industrial control products, systems and services. The wiring of both is same. 3-phase AC Panel Load Calc. 3000W / 240V = 12. Home / Technical Articles / Sizing The DOL Motor Starter Parts (Contactor, Fuse, Circuit Breaker and Thermal Overload Relay) Calculate size of each part of DOL motor starter for the system voltage 415V, 5HP three phase house hold application induction motor, code A, motor efficiency 80%, motor RPM 750, power factor 0. Annexes Annex 1 on TRV Annex 2 on New Test Procedure T100a Annex 3 on Transformer Limited. Characteristics of electric arc. When the substation circuit breaker is replaced by a combined circuit breaker and mechanically interlocked grounding switch, the voltage on Phase B (Green Trace) rise to about 1. kindly help me. Three Phase Equations & Heater Wiring Diagrams Open Delta & Wye Three phase heating circuits are most efﬁ cient when operated under balanced conditions. This is good for 50 amp rated unit. The large transmission substations can cover a large area (several acres/hectares) with multiple voltage levels, many circuit breakers and a large amount of protection and control equipment. Statistics. Calculate Size of each Part of Star-Delta starter for 10HP, 415 Volt Three Phase Induction Motor having Non Inductive Type Load, Code A, Motor efficiency 80%, Motor RPM 600, Power Factor 0. The (Blue Trace) shows the transient and temporary overvoltage on Phase B with a conventional breaker and a grounding transformer in the circuit. ARCO Electric Products uses 3 Pole molded case circuit breakers to protect each of the switched capacitor stages in the automatic unit. 1 Pole Single phase circuits. Cable size Circuit breaker amp size How to calculate What cable - Duration: 13:01. In terms of load sizing, this means that each phase (of the 3 phase electrical supply) will deliver upto 40KVA (or 174Amps at 230Vac). 3-phase Supply Division or balancing of Loads – Balanced phases – Transformer Sizing implications – Cable sizing implications – Neutral Current implication Advantages of a 3-Phase System: – Dual Voltage – Machine physicality's – Rotational Magnetic Fluxes in Machines – Transmission. How to convert kw to amps in 3 phase system - Duration: 1:25. Three wire, 100 amp. 5 20 12 40 35 2 24 10 50 40 3 34 8 70 60 5 56 4 90 100 7. In below image i shown that how to wire 3 pole C breaker with 3 phase supply. The copper THHN circuit conductors are routed in an area with an ambient temperature not exceeding 104°F, and the number of current-carrying conductors in the raceway is three. of Phases Single Phase Three Phase. This is from Digest 176, page 7-33, dated 2012. Wire size for 100 amp 3 phase circuit [ 1 Answers ] I am installing a commercial convection oven rated as follows: 220V 3 Phase. and you can simply round up to the next higher size of the breaker. So, for 14. Get it as soon as Tue, Jun 30. 8 Amps, so i need a 50 Amp breaker. The main distinctions between molded-case and miniature circuit breaker are that the MCCB can have current ratings of up to 2,500 amperes, and its trip settings are usually adjustable. I jump in cycles to the 1984 cycle for the first time a voltage is mentioned in;. 33A So the current load for each phase. The next higher standard-size circuit breaker is 20 amperes. Voltage is the measurement of differences in electric potential energy. Note: maximum earth fault loop impedance for devices listed in BS 7671 is available for 0. 5 80 3 110 150 10 100 — — 175 115V Single Phase Motors HP FLA* Wire Circuit Breaker Size RK5 Fuse Heavy Load 1 2. Mohamed - The current is for each phase. May 01, 1996. 3-Phase Voltage Drop Calculator with Power Factor: This JavaScript calculator runs in a web page. To calculate the size of the three-phase dedicated panel breaker, the single-phase currents must be calculated. Distribution boards and Protection devices ppt 1. Single & Three Phase Line kVA calculator is an online tool used in electrical engineering to measure the unknown quantity by two known quantities applied to the below formulas for single phase and three phase connection. Hi, i'm a little confused about the way to calculate the amp of the circuit breaker for a three-phase system. 5 kW and voltage of 400V, what size circuit breaker is needed for three-phase system. relays, the time interval is usually 0. For example, the full-load current of a 5 HP motor at 460V is 7. Three phase A/C turbines are more efficient in transmission of power to the batteries when the three phase rectifier is located near the batteries, so we will address 3 phase in a separate section. Amps to kW calculator;. FC 2 Mobile App Quickly Delivers Fault Current Calculations in the Palm of Your Hand. CHART TO DETERMINE FUSE / BREAKER AND WIRE SIZES FOR ELECTRIC MOTORS (For single phase A. Phase shifting transformers to control power flow between two adjacent power systems. source but with one phase connected to wound. 0 amps for 250 feet on a 240 volt system. Here first I am sharing with the main wiring diagram. Tel + 27 11 928 2000 • Fax + 27 11 392 2354 EBM – Class 1, single and 3 phase energy meters. In recent years, extending 3-phase power distribution all the way to server cabinets and racks has become extremely popular in new data center builds—for many good reasons. 5 kW and voltage of 400V, what size circuit breaker is needed for three-phase system. In a real transformer, due to losses, the power at the secondary coil will always be smaller than the power at the primary coil. Electrical Calculations is the best app in the electrical sector, it has many calculations that can help you in your work. This is in contrast to the values of the short-circuit current under conditions according IEC 62271-100 , which is 25 % of the rated short circuit current. 450-3b, 240-3, 240-21, 384-16d, 430-72b Ex. 2013, Chennai, India ISBN: 978-93-82702-28-3 98 Stability [2] studies are performed in order to be sure that the system will remain stable following a severe. 35 do not apply to panelboards 3-Phase, 3-wire 3-Phase, 3-wire 3-Phase, 4-wire 3-Phase, 3-wire 3-Phase, 3-wire. Power Load Calculator. This calculates to 63+ kVA, thus we round up to a standard Three Phase size 75kVA. Lets take a load that needs a power rating of 10kW and on voltage of 415V. 3 for feeder overcurrent protection). The three circuit breakers are tested at different angles. 8 Amps, so i need a 50 Amp breaker. The alternator has a line voltage of 480 V. circuit breaking requirements of good circuit breaker circuit breaker rating. 3 amps,(per phase) but a single phase 30 amp breaker will carry 30 amps And if that were true, 3 pole 30amp breakers would be marked 17 amps. They can be combined with our NEMA and IEC motor starters, overload relays, and contactors. Determine the MAXIMUM standard size time-delay fuses permitted for branch-circuit, short-circuit and ground-fault protection for a 50 hp, 3-phase, 480-volt, induction-type motor with a full-load ampere rating of 61 amperes marked on the nameplate. and you can simply round up to the next higher size of the breaker. The circuit breaker quickly protects the distribution against shorts circuits essentially. An inverse time circuit breaker used as the disconnecting means for a 50 hp, 480-volt, three-phase continuous-duty, induction-type ac motor shall have an ampere rating of at LEAST _____. SO Generator set without on-load tap changer. Rating of a Three Phase Transformer. (2) Thermal Setting of Circuit Breaker: 1. To find the breaker size for three phase supply voltage, we must know the exact kind of load as there are many factors affecting the load current. thermal unit. To calculate kVA, you need to enter the known values of voltage and the current into the respective fields. For example if you are calculating the size of cable for a 1 kW single phase pump. The OP does reference 430. 7 amps current pull. 208V 3 Phase Power Panel. There are a lot of factors that need to be. Zup Equivalent impedance of the upstream network. I jump in cycles to the 1984 cycle for the first time a voltage is mentioned in;. Calculation size of circuit breaker and fuse are as per NEC 450. That’s because Goodman lives up to its name in a big way, with time-tested energy-efficient technology, highly durable materials and spot-on manufacturing. They also protect circuits downstream from the transformer. The feeder breaker to the. Conduit sizes may need to be increased if equipment grounding conductors or neutrals are also installed in the conduit. 75%6 = 11 Amp. Often, the result is not a common circuit breaker size. How To Calculate The Cable Size Of A Motor By Using Kw Quora 3 10 three phase feeder size schedule engineering360 electrical cable wire sizing engineering centre square d overload size chart batan vtngcf org further electrical dimensional parameters for panel boards. Rating of Circuit Breaker =2000Amp (Next Higher Size of 1600Amp) Size of Fuse = 1342. There is no magnetic connection between single-phase units, only electric bus or cable interconnection exist between individual units. 8) Therefore –. Circuit Breakers: Formation of arc during circuit breaking. 55 to calculate a rating of 33. You will see 2 measurements listed: The first will tell you the wire gauge, followed by a dash and a second number which indicates how many wires are inside the cable. 4 Pole Three phase circuits with neutral. 100, accessories: auxiliary contact, voltage release. It is an international clearing house, with 180,000 square facility located in Hayward, California. The feeder breaker to the. 73 Gnd OV A-Gnd Fault on Ungrounded System 1. For example, if the load calculation comes out to 48 amps, you should use a 50-amp breaker to protect the circuit. AC three phase amps to kilowatts calculation formula. Unfollow circuit breaker 50 amp to stop getting updates on your eBay Feed. Divide kW by the power factor to get the kVA. 73 Gnd OV A-Gnd Fault on Ungrounded System 1. In the first case, each inverter is attached to a single line of the three phase system. 5 Amperes, Use 30 A Circuit Breaker [3] Conduit = Use 3/4" diameter PVC conduit. In the main panel, every other breaker is out of phase with the adjoining breakers. 3-Phase Induction Motors. ) FLA=\frac{S_1\phi}{V_{line}} Figure 1: Calculation of short circuit rating of a single phase breaker. It keeps an extensive inventory of electrical connectors, conduit fitting, circuit breakers, junction boxes, wire cable, safety switches etc. Three Phase Equations & Heater Wiring Diagrams Open Delta & Wye Three phase heating circuits are most efﬁ cient when operated under balanced conditions. A 1500-watt heater on a 120-volt circuit thus needs a breaker of 15. distance about 110feet. A "continuous load" is one where the maximum current is expected to continue for three hours or more. (Vline) 240V Vphase What size circuit breaker is needed for three-phase system? P = 3 x VPH x IPH x CosФ P = √3 x VL x IL x CosФ If I use phase values do I need to divied the power by 3 (1000/3) before using the formula ? Does it matter how the three phase system is connected Star or Delta ? My calculation was 1000. Square D® is a global brand of Schneider Electric for NEMA-type electrical distribution and industrial control products, systems and services. It assumes the motor gets to speed quickly (a few seconds at most), or has a starter to reduce current during starting if it is taking too long. circuit breaking requirements of good circuit breaker circuit breaker rating. As a result, 52Y would be de-energized, which would close 52Y/2 and open 52Y/1. kVA is used to compute what size wiring you need, what size breaker, etc, to power a circuit of a given amperage/wattage. • Similar Requirements in OSHA 1910. 732x400) = 16. Including the new WS-V series equipped with the latest breaker technology, various product ranges are available that address the needs of both the power incoming panel / distribution board market and machinery market. A slash rating such as 120/240V indicates that the breaker cannot be used where the voltage to ground on a circuit conductor exceeds 120V. 85, KVA code: H. 25, reference 430. Voltage (V): Specify the voltage and select the phase arrangement: 1 Phase AC or 3 phase AC. The wiring to the appliance also needs to be changed. The cable sizing calculator calculates the cable size according to AS/NZS 3008. The wire size returned was 4 mm^2. Sizing Calculator (Just plug in your machine info and the calculator picks the correct size) 2. but i dont know how to enter voltage range for 3 phase. Let's say we're using a SolarWorld 315 Watt module with an ISC rationg of 9. 679 results for 3 phase breaker Save 3 phase breaker to get e-mail alerts and updates on your eBay Feed. Calculation size of circuit breaker and fuse are as per NEC 450. Call us at (800) 540-7821. 240 x 25 x 3 = 18 kW. The dryer cable should have four wires, including the dedicated ground wire. Three pole RCCB is preferred only for two phase neutral system. In terms of load sizing, this means that each phase (of the 3 phase electrical supply) will deliver upto 40KVA (or 174Amps at 230Vac). Using SWR 1800U or SB 700U inverters in a 208 WYE system or using SB 6000U inverters in a 480. 4 14 15A 15A ½ 208V / 230V 4. Circuit Breaker Current Rating. The back panel of the dryer specifies the size of breaker it requires, but most use a 30-amp breaker. If your total 3-phase load in a 480V system is 50,000VA, what size breaker do you need? 50,000VA ÷ (480V × 1. relays, the time interval is usually 0. In the first case, each inverter is attached to a single line of the three phase system. k2 Phase-to-phase short circuit. Phase shifting transformers to control power flow between two adjacent power systems. Calculator description. 99 % Advantages. " The input of the Rack PDU is actually limited by the internal circuit breakers. Final Filter 3: If the MOP is less than 15, it shall be rounded up to 15 amps. REVIEW: The poor power factor in an AC circuit may be “corrected”, or re-established at a value close to 1, by adding a parallel reactance opposite the effect of the load’s reactance. In the main panel, every other breaker is out of phase with the adjoining breakers. When placing multiple heaters on a circuit do not exceed the wattage listed for the corresponding wire and circuit breaker size. This is very useful when you are in pre-production as you will easily be able to calculate in advance whether or not you will need an external generator, and how many. ) Single Phase BREAKER SIZE WIRE SIZE Based on copper THHN wire – increase one size when using aluminum conductors AT 115 VOLTS AT 230 VOLTS 15 amp #14 1,380 2,760 20 amp #12 1,840 3,680 30 amp #10 Seldom used on 115 voltage 5,520 40 amp # 8 Seldom used on 115 voltage 7,360 50 amp #6 Seldom used on 115 voltage 9,200 *60. The figure we would plug into the calculator would be: (40 x 1. Current chopping. I= P(W) / (Voltage * Power factor). Since each phase circuit is equal to the others, the 3 phases will be balanced and doing calculations for only one phase will be enough. 2P in 1 module, 3 and 4P in 2 modules Complete range: from 4. This will set the pattern to be used in other cases. (I2) = the current at which the CB opens. The Design Engineer should consider the following points while doing 'BUSBAR SIZING CALCULATION': Adequate minimum required clearance between Phases and Phase to Earth. Shunt reactors with a saturable core could also be possible. (It) = tabulated current for a single circuit at ambient temp of 30° (Ib) = the actual current to be carried. The breaker will carry in the ambient temperature where it was calibrated. Final Filter 3: If the MOP is less than 15, it shall be rounded up to 15 amps. 3 for feeder overcurrent protection). Circuit breakers are sized to protect the wiring of your structure, not the utilization equipment. Re: How to Calculate Incomer Breaker Sizing for a 3 Phase 4 Wire 415V 50Hz UPS DB 07/01/2013 6:09 AM Otherwise, if what you meant is the incomer at the UPS incomer, the average current per phase of a 3 phase 10KVA UPS is 14A @ 415VAC and unity power factor. It's fine to exceed this for short periods of time, but continuous current above this amount could cause enough heat to trip the breaker. How to Convert kVa to KW for Generators. Size of Circuit Breaker Circuit Breaker as per NEC 430-52 Type of Motor Instantaneous Trip Inverse Time Single Phase 800% 250% 3 Phase 800% 250% Synchronous 800% 250% Wound Rotor 800% 150% Direct Current 200% 150% Maximum Size of Instantaneous Trip Circuit Breaker = 800% x Full Load Line Current. I am trying to size a circuit breaker for a transformer. 9 14 15 5-6/10 1. Cummins is a world leader in power generation equipment, including PowerCommand™ standby and prime power systems. Select transformer phase. Wire Size Awg No. my breakers are as follows 1-200 amp 1-150 amp 3-125 amp 3-100 amp 5-80 amp 1-50 amp 1-40 amp 1-30 amp all these add up to 1545 amps. A 208V 3 Phase Power Panel provides 3 power circuit types (120V 1 Phase, 208V 1 Phase, 208V 3 Phase) in 7 circuit configurations based on Circuit Breaker (CB) Type (1 Pole, 2 Pole, 3 Pole) and Position (1, 2, 3, etc. Current (I): Enter the the current in Amperes (A). Single-phase voltages are usually 115V or 120V, while three-phase voltages are typically 208V, 230V or 480V. The alternator has a line voltage of 480 V. Breaker Size Three Phase Full Load Running AMPS: 460/480 volt Three Phase Start Up AMPS: 460/480 volt Breaker Size Motor HP 2 10 20 N/A 3 15 30 N/A. 250 for3 phases motor at voltage and horse power you can select flc or starting current Second step to calculat cable size: flc *1. panel schedule software for Commercial and Industrial Applications Panel 2020 is a full function design package that will simplify the time consuming task of preparing panel schedules, load calculations, and circuit directories. So we have to select a Motor circuit breaker having current range in that value. 33 amperes, the circuit cannot be less than 40 amperes. This free voltage drop calculator estimates the voltage drop of an electrical circuit based on the wire size, distance, and anticipated load current. If i have a power of 11. Often, the result is not a common circuit breaker size. Step 3: Select Conductor Type and Raceway Characteristics from the drop down box. Other models accept a wide range of fuse types, including Siemens exclusive three-pole circuit breaker shall be considered three over current devices. Arc Extinction Principles 7. 2P in 1 module, 3 and 4P in 2 modules Complete range: from 4. Three pumps of a pump station (30, 10, and 1 ½ horsepower) are connected to the power source of 460-volts, 3-phase. The 3 phase Induction motor is popular for its efficiency and is widely employed in the electric systems for doing […]. Calculation size of circuit breaker and fuse are as per NEC 450. So, for 14. This article will list those 4 methods and then give a short description of each method. The consumer unit is a hager and I was wondering what size breaker What size armoured cable do I need for my summerhouse and 32amp hot tub. 6 V to be used when applying the Formula. Instructions below:-1. For a basic project in zip code 47474 with 6 breakers, the cost to Install a Circuit Breaker starts at $190 -$226 per breaker. Circuit Wiring - Single Phase 230V Electrical Motors. -Two values of the short-circuit current must be evaluated 1-The maximum short-circuit current, used to determine: A-The breaking capacity of the circuit breakers B-The making capacity of the circuit breakers 2-The minimum short-circuit current, essential when selecting the time-current curve for circuit breakers and fuses, in particular when. 5kV and ratings up to 5000kVA (ONAN), Prolec GE compartment-type Three-Phase Pad-Mounted Commercial Transformers are designed for outdoor installation on a concrete pad and provide underground power distribution to commercial. 3-phase Supply Division or balancing of Loads – Balanced phases – Transformer Sizing implications – Cable sizing implications – Neutral Current implication Advantages of a 3-Phase System: – Dual Voltage – Machine physicality's – Rotational Magnetic Fluxes in Machines – Transmission. For single phase load two pole RCCB is used and for Three phase 4 wire loads, four pole RCCB are preferred. The copper THHN circuit conductors are routed in an area with an ambient temperature not exceeding 104°F, and the number of current-carrying conductors in the raceway is three. Step One: Single Phase or Three Phase Application IF Three Phase: Three wire source: Must use Open Delta; Four-wire source: Use Open Delta if only need three wires for load. miniature circuit breakers which, in the UK, have been manufactured since 1965 to BS 3871, under the title ‘Miniature Air Circuit Breakers for a. ) and 240 V to 600 V. motors only) 1. MCB Current Calculation, OLR, Fuses and Cable size Calculations for 20 Hp Three phase (TP) Induction Motor. 247 through 430. Type of Load : Three Phase Induction Motor 20 Hp, LL- 400V, 0. Platform: Windows; Publisher: Squigmund Productions; Date: Size: 1024 KB. 4 14 12A / 10A 15A 1 115V 12. We will first analyze wiring size for solar panels and D/C turbines. According to your logic, a 3 phase 30a breaker will only carry 17. This technical brief goes through a step by step process of adding one load at a time to a 120/240 V AC system and looking at the resulting current flows. kindly help me. 3 Phase (480 volt @ 60Hz) 1 Phase (240 volt @ 60Hz) Starting Sequence the above calculations are an estimate only because other factors such as site conditions. Note: If you had a 3-phase transformer, the formula would be Iprimary = KVA x 1000/(Vprimary x 1. 3 (B), NEC 240. 8 14 25 25 1 16 14 30 30 1. three-phase fault. Two regulators connected in open-delta to a 3-phase system, on the other hand, will always. (287 X 6 = 1722 amps) This setting is achieved by adjusting the instantaneous unit adjustable core screw. This cable sizing calculation program allows you to calculate cable size based on electric motor minimum allowable starting voltage. The number of 500 kV substations in the. ) FLA=\frac{S_1\phi}{V_{line}} Figure 1: Calculation of short circuit rating of a single phase breaker. Single-phase units have individual core and coils. I need to buy a breaker for this and don't know what size to buy. All your cables, for all your projects. 60 and 90. The next size up is 70A. 4 Fire Pumps, Voltage Drop (mandatory calculation) 6. Used: for Three Phase circuit; 3 Pole with Neutral (TPN (3P+N) MCB): A TPN MCB, has switching and protection to all three phases of circuit and additionally Neutral is also part of the MCB as a separate pole. I'm thinking of using the A-C legs to one condenser and and B-C legs to the other Assuming I don't exceed the breaker amperage, will the excess amperage on the C leg foul up the. 0 out of 5 stars 2. Main Breaker Trips • Remove the lightning arrestors and try again. 25, reference 430. 25 for wire sizing. CHART TO DETERMINE FUSE / BREAKER AND WIRE SIZES FOR ELECTRIC MOTORS (For single phase A. 732x400) = 16. Here first I am sharing with the main wiring diagram. 73 times your three phase so at peak you are at about 173 amps, I would put in 3/0 if you are close to the single phase panel. To calculate kVA, you need to enter the known values of voltage and the current into the respective fields. The next higher standard-size circuit breaker is 20 amperes. 15 when starting current is not a problem. How To Calculate The Cable Size Of A Motor By Using Kw Quora 3 10 three phase feeder size schedule engineering360 electrical cable wire sizing engineering centre square d overload size chart batan vtngcf org further electrical dimensional parameters for panel boards. Down-sizing S mart wiring Wiring reduction S AC Three-Phase Motor (AC-3) IEC Motor Circuit Breakers 200/240V 400/415V 440/460V 500V Model Name Heater Designation. 5 A on the secondary winding. A wye-connected three-phase alternator supplies power to a delta-con-nected resistive load, Figure 12-17. 5 Elevator Feeder Demand Factors 6. 73 is 87 amps. The combined kVA of three single-phase regulators connected in grounded wye will always be equal to the three phase regulator kVA for the system. Description. What is power consumption in kW when the power factor is 0. The power taken by a circuit (single or three phase) is measured in watts W (or kW). 8 14 15 12 0. You want to power up 24 X 2000 Watt 120 volt Tungsten bulbs, with 8 bulbs on each phase; this means that the current on each phase will be: Ip = 8 * 2000W / 120V = 133. Feeder circuits supplying subpanels are 240-volt and require a double-pole circuit breaker. 52; 21A x 2. Short circuit current is usually supplied from utility transmission system, generators, and synchronous and induction motors. Fuse sizing is calculated by the size of the conductor. thermal breaker size. (287 X 6 = 1722 amps) This setting is achieved by adjusting the instantaneous unit adjustable core screw. one melting alloy thermal unit. For example, the magnitude of the currents may be needed to properly size conductors, conduits, relays, fuses, circuit breakers, transformers and the like. 6 - Ok - I want to run the 3 phase motor. 3 as well as size of transformer and transformer full load losses. Multiply the value for current by 125 percent to determine the size of the breaker you need for the heater. These rating are adequate for runs of up to appx 60 ft. Please check with your electrical inspector or a licensed electrician for the proper wire size. 6 Calculation Example: 3-Phase Short-Circuit Current % impedance method Ohmic method The supply short-circuit capacity, being unknown, is The supply short-circuit capacity, being unknown, is defined as 1000MVA with X = 25. 8, Overload Relay of Starter is Put before Motor. It is used for sizing wiring, circuit breakers, and UPS (uninterruptible power supply). Acme Electric manufactures innovative power conversion and conditioning equipment for industrial, commercial and OEM applications. If your total 3-phase load in a 480V system is 50,000VA, what size breaker do you need? 50,000VA ÷ (480V × 1. Unibis* compact MCBs are one of the latest introductions in the Redline range and are developed to reduce the size of the distribution board to the minimum. The Stator consists of three-phase windings overlapped with one another at a 120-degree phase shift. If we draw a circuit showing each voltage source to be a coil of wire (alternator or transformer winding) and do some slight rearranging, the “Y” configuration becomes more obvious in Figure below. The next higher standard-size circuit breaker is 20 amperes. 6 Amps per phase 16. Get free shipping on qualified 3 Pole Breakers or Buy Online Pick Up in Store today in the Electrical department. To close the circuit breaker, control power would have to be removed by resetting the remote close switch to the open position. E-Coord - Perform fuse and breaker coordination studies and select equipment. Used: for Three Phase circuit; 3 Pole with Neutral (TPN (3P+N) MCB): A TPN MCB, has switching and protection to all three phases of circuit and additionally Neutral is also part of the MCB as a separate pole. how do you calculate the cable size and breaker size? lets say for example fryer is 9. I am trying to size a circuit breaker for a transformer. When connected in series with three-phase elements, it returns the three phase-to-ground or phase-to-phase peak voltages and currents. In other words, the breaker controlling a circuit should be 125 percent of the continuous load (maximum current expected to last for three hours or more) and 100 percent of the non-continuous load. Size of Circuit Breaker = 1342. 3 and NEC 240. 52 do not correspond to the standard sizes or ratings of fuses, nonadjustable circuit breakers,thermal protective devices, or possible settings of adjustable circuit breakers, a higher. 3-phase Supply Division or balancing of Loads – Balanced phases – Transformer Sizing implications – Cable sizing implications – Neutral Current implication Advantages of a 3-Phase System: – Dual Voltage – Machine physicality's – Rotational Magnetic Fluxes in Machines – Transmission. Allowable Voltage Drop. So, in essence 240 volt wiring is powered by 2 - 120 volt hot wires that are 180 degrees out of phase. Conductor Size: Motor branch-circuit short-circuit and ground-fault protection (percentage of FLA from Tables 430. 100, accessories: auxiliary contact, voltage release. Step 1 Three Phase - Find the FLC (full load current) - Table 430-150 three phase Step 2 Branch Circuit Conductor Sizing - 430-22 Single Motor: Calculate 125% of FLC = Ampacity - Turn to 310-16 to find the wire size. Generator Sizing kVa Calculator. When sizing conductors, calculations limits wire size to voltage drop and NEC ampacity. SIZE I ,SIZE II or SIZE III, Normal Current carrying capacity, Breaking capacity of contacts in kilo Ampere like 65 KA,80 KA,100 KA. 7 Fixed Electric Heating Equipment for Pipelines and Vessels, Branch-Circuit Sizing 4. The procedure in determining the short-circuit rating of a 1-phase circuit-breaker in a 1-phase system is same as above except for the modification to the full load current equation (of the 1-phase transformer. How would you go about determining the size of conducter needed to feed this building> if you where to perform a load calculation and then use wire acording to the calculation how would you make sure that later on nobody would come alonge and just add circuits. 0 MultI-WIrE BrANCh CIrCuItS As explained above, in a utility-connected, 120 / 240 VAC Single Split Phase System, the 120 / 240 VAC power consists of two 120 VAC lines. Note that some types of single-phase loads are routinely supplied by a 3-phase panel. 9 14 15 5-6/10 1. It is not to be relied upon. I'm looking at how to calculate a breaker for a three-phase circuit. Brandnew design. 4 14 12A / 10A 15A 1 115V 12. “Short Circuit MVA” is the rupturing capacity or breaking capacity of a circuit breaker in case of a three phase symmetrical fault which determines the size of the circuit breaker. -Two values of the short-circuit current must be evaluated 1-The maximum short-circuit current, used to determine: A-The breaking capacity of the circuit breakers B-The making capacity of the circuit breakers 2-The minimum short-circuit current, essential when selecting the time-current curve for circuit breakers and fuses, in particular when. The 3 phase Induction motor is popular for its efficiency and is widely employed in the electric systems for doing […]. All about Motors Page Motor protection 8-3 Notes on engineering 8-15 Circuit documents 8-19 Power supply 8-21 Control circuit supply 8-24 Contactor markings 8-25 Direct-on-line start of three-phase motors 8-26 Control circuit devices for direct-on-line start 8-34 Star-delta switching of three-phase motors 8-35. Each leg is 50 amps @ 120 volts. 240V power circuits. An example would include '120KVA three phase'. (415v or 220v). AC three phase amps to kilowatts calculation formula. Rating of Circuit Breaker =2000Amp (Next Higher Size of 1600Amp) Size of Fuse = 1342. 7 Extending a three-phase short-circuit calculation procedures program the circuit protective devices—the circuit breakers and fusible switches. To calculate the maximum wattage of the circuit breaker, multiply the amperage by 120V. Note: This is a sample kVA calculation and does not take into account possible special load requirements, such as found with motors or some medical equipment, or other specialty applications. Conduit sizes are for three conductors per circuit for three phase motors and two conductors per circuit for single phase and DC motors. You hire a licensed Electrical Engineer. How am I going to size my 3 phase X'mer with 1 phase load using current as reference [ 3 Answers ] Hi, I'm Peping: I have 90 pieces of single phase loads with current of 2 Amperes. 100% rated solutions for a circuit breaker will have a frame size no smaller than 250 Amps at 250 volts and below, or any case size for multi-pole circuit breaker with a voltage greater than 250 V. Currently supports AC only. Allowable Voltage Drop. Get it as soon as Tue, Jun 30. fractional hp n1 starter class 2510. Circuit breakers are used in conjunction with protective relays to protect circuits from faults. These conditions, per UL 489, Underwriters Laboratories Standard for Safety for Molded-Case Circuit Breakers and Circuit Breaker Enclosures, include mounting the CB in free air (i. Determine the main feeder of the motors. Calculate Size of each Part of Star-Delta starter for 10HP, 415 Volt Three Phase Induction Motor having Non Inductive Type Load, Code A, Motor efficiency 80%, Motor RPM 600, Power Factor 0. The 30-amp breaker requires 10-gauge wires. The breaker will carry in the ambient temperature where it was calibrated.

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# Right Regular Pyramid, Surface Area Formula

The most common type of pyramid usually encountered in Math at a more basic level, is a right regular pyramid with a square base, and the top/apex directly above the centre of the base.

Some examples of working out the area of such a shape are shown on the surface area of a pyramid page.

However, there is a more general surface area formula that can be used to establish the surface area of any right regular pyramid, even with base shapes different to a square.

For a right regular pyramid such as the one in the image above, where the top is above the centre of the base, and the base is a regular polygon with each side the same length.

To get the total pyramid surface area, we want to add the base area to the lateral area of the side faces.

The base area is usually straight forward to work out when the base is a regular polygon.

But also, the area of the side faces all together can be given by:

$\dpi{80}&space;\fn_jvn&space;\frac{1}{2}$  x  perimeter  x  slant height,     ( $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$ps )

Let's see how this sides surface area formula comes about.

For a regular right pyramid, with a base where each side is the same length a, and each side face also has the same slant height as each other s.

Each face on its own is a triangle, so the area of just 1 face is given by the standard area of a triangle formula,  $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$ x a x s.

How many sides the base has, will determine how many triangle side faces there are in the whole pyramid shape.

n = number of sides

n sides  =  n triangles.

Meaning that the area of all the faces is given by  ( number of sides ) x $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$ x a x s.

n x $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$ x a x s    for short.

This form can actually be re-ordered slightly to   n x a x $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$ x s.

It just happens that the perimeter of a regular polygon base is given by   n x a.

( number of sides n ) x ( length of 1 side a )

SQUARE BASE EXAMPLE

So,   n x a x $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$ x s   =   p x $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$ x s    or    $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$ x p x s           ( p = perimeter )

Resulting in a more general formula for the surface area of a regular right pyramid:

Area  =  ( BASE AREA )  +  ( $\dpi{80}&space;\fn_jvn&space;{\color{DarkGreen}&space;\frac{1}{2}}$ x Perimeter x Slant-Height )

## Surface Area Formula Examples

(1.1)

Area  =  ( BASE AREA )  +  ( $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$PS )

BASE AREA   =>   5 x 5  =  25m2

$\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$PS   =>   $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$ x 20 x 7  =  70m2

Area  =  25m2 + 70m2  =  95m2

(1.2)

Area  =  ( BASE AREA )  +  ( $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$PS )

Base is an equilateral triangle.

BASE AREA   =>   $\dpi{70}&space;\fn_jvn&space;\frac{\sqrt{3}}{4}$(4)2  ≈  6.93m2

$\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$PS   =>   $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$ x 12 x 5  =  30m2

Area  ≈  6.93m2 + 30m2  ≈  36.93m2

(1.3)

Area  =  ( BASE AREA )  +  ( $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$PS )

Base is a regular Pentagon.

BASE AREA   =>   Roughly  ≈  6.88cm2

$\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$PS   =>   $\dpi{70}&space;\fn_jvn&space;\frac{1}{2}$ x 10 x 6  =  30cm2

Area  ≈  6.88cm2 + 30cm2  ≈  36.88cm2

This surface area formula will also work for other right pyramids where the base is a regular polygon with all sides of equal length.

›   ›  Surface Area, Right Regular Pyramid


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Elementary Algebra 2e

# 4.3Graph with Intercepts

Elementary Algebra 2e4.3 Graph with Intercepts

### Learning Objectives

By the end of this section, you will be able to:

• Identify the x - and y - intercepts on a graph
• Find the x - and y - intercepts from an equation of a line
• Graph a line using the intercepts

### Be Prepared 4.6

Before you get started, take this readiness quiz.

Solve: $3·0+4y=−2.3·0+4y=−2.$
If you missed this problem, review Example 2.17.

### Identify the x- and y- Intercepts on a Graph

Every linear equation can be represented by a unique line that shows all the solutions of the equation. We have seen that when graphing a line by plotting points, you can use any three solutions to graph. This means that two people graphing the line might use different sets of three points.

At first glance, their two lines might not appear to be the same, since they would have different points labeled. But if all the work was done correctly, the lines should be exactly the same. One way to recognize that they are indeed the same line is to look at where the line crosses the x- axis and the y- axis. These points are called the intercepts of the line.

### Intercepts of a Line

The points where a line crosses the x- axis and the y- axis are called the intercepts of a line.

Let’s look at the graphs of the lines in Figure 4.18.

Figure 4.18 Examples of graphs crossing the x-negative axis.

First, notice where each of these lines crosses the $xx$ negative axis. See Figure 4.18.

 Figure The line crosses the x- axis at: Ordered pair of this point Figure (a) 3 $(3,0)(3,0)$ Figure (b) 4 $(4,0)(4,0)$ Figure (c) 5 $(5,0)(5,0)$ Figure (d) 0 $(0,0)(0,0)$
Table 4.24

Do you see a pattern?

For each row, the y- coordinate of the point where the line crosses the x- axis is zero. The point where the line crosses the x- axis has the form $(a,0)(a,0)$ and is called the x- intercept of a line. The x- intercept occurs when $yy$ is zero.

Now, let’s look at the points where these lines cross the y- axis. See Table 4.25.

 Figure The line crosses the y-axis at: Ordered pair for this point Figure (a) 6 $(0,6)(0,6)$ Figure (b) $−3−3$ $(0,−3)(0,−3)$ Figure (c) $−5−5$ $(0,−5)(0,−5)$ Figure (d) 0 $(0,0)(0,0)$
Table 4.25

What is the pattern here?

In each row, the x- coordinate of the point where the line crosses the y- axis is zero. The point where the line crosses the y- axis has the form $(0,b)(0,b)$ and is called the y- intercept of the line. The y- intercept occurs when $xx$ is zero.

### x- intercept and y- intercept of a line

The x- intercept is the point $(a,0)(a,0)$ where the line crosses the x- axis.

The y- intercept is the point $(0,b)(0,b)$ where the line crosses the y- axis.

### Example 4.19

Find the x- and y- intercepts on each graph.

### Try It 4.37

Find the x- and y- intercepts on the graph.

### Try It 4.38

Find the x- and y- intercepts on the graph.

### Find the x- and y- Intercepts from an Equation of a Line

Recognizing that the x- intercept occurs when y is zero and that the y- intercept occurs when x is zero, gives us a method to find the intercepts of a line from its equation. To find the x- intercept, let $y=0y=0$ and solve for x. To find the y- intercept, let $x=0x=0$ and solve for y.

### Find the x- and y- Intercepts from the Equation of a Line

Use the equation of the line. To find:

• the x- intercept of the line, let $y=0 y=0$ and solve for $xx$.
• the y- intercept of the line, let $x=0x=0$ and solve for $yy$.

### Example 4.20

Find the intercepts of $2x+y=62x+y=6$.

### Try It 4.39

Find the intercepts of $3x+y=12.3x+y=12.$

### Try It 4.40

Find the intercepts of $x+4y=8.x+4y=8.$

### Example 4.21

Find the intercepts of $4x–3y=124x–3y=12$.

### Try It 4.41

Find the intercepts of $3x–4y=12.3x–4y=12.$

### Try It 4.42

Find the intercepts of $2x–4y=8.2x–4y=8.$

### Graph a Line Using the Intercepts

To graph a linear equation by plotting points, you need to find three points whose coordinates are solutions to the equation. You can use the x- and y- intercepts as two of your three points. Find the intercepts, and then find a third point to ensure accuracy. Make sure the points line up—then draw the line. This method is often the quickest way to graph a line.

### Example 4.22

#### How to Graph a Line Using Intercepts

Graph $–x+2y=6–x+2y=6$ using the intercepts.

### Try It 4.43

Graph $x–2y=4x–2y=4$ using the intercepts.

### Try It 4.44

Graph $–x+3y=6–x+3y=6$ using the intercepts.

The steps to graph a linear equation using the intercepts are summarized below.

### How To

#### Graph a linear equation using the intercepts.

1. Step 1. Find the x- and y- intercepts of the line.
• Let $y=0y=0$ and solve for $xx$
• Let $x=0x=0$ and solve for $yy$.
2. Step 2. Find a third solution to the equation.
3. Step 3. Plot the three points and check that they line up.
4. Step 4. Draw the line.

### Example 4.23

Graph $4x–3y=124x–3y=12$ using the intercepts.

### Try It 4.45

Graph $5x–2y=105x–2y=10$ using the intercepts.

### Try It 4.46

Graph $3x–4y=123x–4y=12$ using the intercepts.

### Example 4.24

Graph $y=5xy=5x$ using the intercepts.

### Try It 4.47

Graph $y=4xy=4x$ using the intercepts.

### Try It 4.48

Graph $y=−xy=−x$ the intercepts.

### Section 4.3 Exercises

#### Practice Makes Perfect

Identify the x- and y- Intercepts on a Graph

In the following exercises, find the x- and y- intercepts on each graph.

139.
140.
141.
142.
143.
144.
145.
146.
147.
148.
149.
150.

Find the x- and y- Intercepts from an Equation of a Line

In the following exercises, find the intercepts for each equation.

151.

$x + y = 4 x + y = 4$

152.

$x + y = 3 x + y = 3$

153.

$x + y = −2 x + y = −2$

154.

$x + y = −5 x + y = −5$

155.

$x – y = 5 x – y = 5$

156.

$x – y = 1 x – y = 1$

157.

$x – y = −3 x – y = −3$

158.

$x – y = −4 x – y = −4$

159.

$x + 2 y = 8 x + 2 y = 8$

160.

$x + 2 y = 10 x + 2 y = 10$

161.

$3 x + y = 6 3 x + y = 6$

162.

$3 x + y = 9 3 x + y = 9$

163.

$x – 3 y = 12 x – 3 y = 12$

164.

$x – 2 y = 8 x – 2 y = 8$

165.

$4 x – y = 8 4 x – y = 8$

166.

$5 x – y = 5 5 x – y = 5$

167.

$2 x + 5 y = 10 2 x + 5 y = 10$

168.

$2 x + 3 y = 6 2 x + 3 y = 6$

169.

$3 x – 2 y = 12 3 x – 2 y = 12$

170.

$3 x – 5 y = 30 3 x – 5 y = 30$

171.

$y = 1 3 x + 1 y = 1 3 x + 1$

172.

$y = 1 4 x − 1 y = 1 4 x − 1$

173.

$y = 1 5 x + 2 y = 1 5 x + 2$

174.

$y = 1 3 x + 4 y = 1 3 x + 4$

175.

$y = 3 x y = 3 x$

176.

$y = −2 x y = −2 x$

177.

$y = −4 x y = −4 x$

178.

$y = 5 x y = 5 x$

Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

179.

$– x + 5 y = 10 – x + 5 y = 10$

180.

$– x + 4 y = 8 – x + 4 y = 8$

181.

$x + 2 y = 4 x + 2 y = 4$

182.

$x + 2 y = 6 x + 2 y = 6$

183.

$x + y = 2 x + y = 2$

184.

$x + y = 5 x + y = 5$

185.

$x + y = −3 x + y = −3$

186.

$x + y = −1 x + y = −1$

187.

$x – y = 1 x – y = 1$

188.

$x – y = 2 x – y = 2$

189.

$x – y = −4 x – y = −4$

190.

$x – y = −3 x – y = −3$

191.

$4 x + y = 4 4 x + y = 4$

192.

$3 x + y = 3 3 x + y = 3$

193.

$2 x + 4 y = 12 2 x + 4 y = 12$

194.

$3 x + 2 y = 12 3 x + 2 y = 12$

195.

$3 x – 2 y = 6 3 x – 2 y = 6$

196.

$5 x – 2 y = 10 5 x – 2 y = 10$

197.

$2 x – 5 y = −20 2 x – 5 y = −20$

198.

$3 x – 4 y = −12 3 x – 4 y = −12$

199.

$3 x – y = −6 3 x – y = −6$

200.

$2 x – y = −8 2 x – y = −8$

201.

$y = −2 x y = −2 x$

202.

$y = −4 x y = −4 x$

203.

$y = x y = x$

204.

$y = 3 x y = 3 x$

#### Everyday Math

205.

Road trip. Damien is driving from Chicago to Denver, a distance of 1000 miles. The x- axis on the graph below shows the time in hours since Damien left Chicago. The y- axis represents the distance he has left to drive.

1. Find the x- and y- intercepts.
2. Explain what the x- and y- intercepts mean for Damien.
206.

Road trip. Ozzie filled up the gas tank of his truck and headed out on a road trip. The x- axis on the graph below shows the number of miles Ozzie drove since filling up. The y- axis represents the number of gallons of gas in the truck’s gas tank.

1. Find the x- and y- intercepts.
2. Explain what the x- and y- intercepts mean for Ozzie.

#### Writing Exercises

207.

How do you find the x- intercept of the graph of $3x–2y=63x–2y=6$?

208.

Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation $4x+y=−44x+y=−4$? Why?

209.

Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation $y=23x−2y=23x−2$? Why?

210.

Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation $y=6y=6$? Why?

#### Self Check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

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# Reusing content

You can put recurring content in a separate file and add it to the necessary places in the document using the construction {% include %}.

Reusing content helps reduce the time spent on editing and searching the source text: information is stored in one place, and changes are automatically applied to all files.

## Instructions for reusing content

1. Create a folder to store recurring content. For example, _includes.

Warning

Images should be stored in a folder whose name starts with _. Otherwise, they will be deleted during the build.

2. In the _includes folder, create a separate MD file with the recurring text.

3. In sections of a document where you need to insert this text, add a link to the file in the following format:

{% include [Description](../_includes/file.md) %}

• [Description]: File description. Information about document authors does not affect the build.
• (_includes/file.md): File path.

If you don't need to add the header of the reusable file to the section, add the notitle keyword:

{% include notitle [Description](../_includes/file.md) %}

When building the document, the text of the file is added to the sections in place of the includes. If there are relative links in the file, they are re-assembled.


text:
# Clarifying $\sum_{h=0}^{\lfloor lg(n)\rfloor}\lceil\frac{n}{2^{h+1}}\rceil O(h)=O(n\sum_{h=0}^{\lfloor lg(n)\rfloor}\frac{h}{2^h})$ in BUILD-MAX-HEAP

I was going the text Introduction to Algorithms by Cormen et. al. Where I came across a step in the analysis of the time complexity of the $$BUILD-MAX-HEAP$$ procedure.

The procedure is as follows:

BUILD-MAX-HEAP(A)
1   heap-size[A] <- length[A]
2   for i <- ⌊length[A]/2⌋ downto 1
3       MAX-HEAPIFY(A,i)

Now the authors claim to derive a tighter bound by observing that the time for $$MAX-HEAPIFY$$ to run at a node varies with the height of the node in the tree, and the heights of most nodes are small. The tighter analysis relies on the properties that an $$n$$-element heap has height $$\lfloor lg (n)\rfloor$$ and at most $$\lceil \frac{n}{2^{h+1}} \rceil$$ nodes of any height $$h$$.

So,$$\sum_{h=0}^{\lfloor lg (n)\rfloor} \lceil \frac{n}{2^{h+1}} \rceil O(h)= O(n \sum_{h=0}^{\lfloor lg (n)\rfloor} \frac{h}{2^h}) \ldots \tag 1$$

Now it is in the above step that I am facing the problem. How are the authors getting the expression on the RHS using the LHS so simply(as if intuitively). However I do not seem to share the same intuition.

Now the maximum height of any node is the height of the root which is $$\lfloor lg (n)\rfloor$$. Now let us find a bound for the minimum possible value of the fraction $$\frac{n}{2^{h+1}}$$ ,which occurs when $$h=\lfloor lg (n)\rfloor$$

So, $$\frac{n}{2^{\lfloor lg (n)\rfloor+1}} = \frac{n}{2.2^{\lfloor lg (n)\rfloor}}\geqslant\frac{n}{2.2^{lg (n)}}=\frac{n}{2n}=\frac{1}{2} \ldots \tag 2$$

Now from the analysis step by the authors in (1) they are assuming

$$\lceil \frac{n}{2^{h+1}} \rceil \leqslant c.\frac{n}{2^h}, c>0$$

Now as far as I know from mathematics,

$$\lceil \frac{n}{2^{h+1}} \rceil \lt \frac{n}{2^{h+1}}+1$$

And for the way the authors worked out , it must be the situation as below,

$$\lceil \frac{n}{2^{h+1}} \rceil \lt \frac{n}{2^{h+1}}+1 \leqslant c.\frac{n}{2^{h}}$$

So, $$\frac{n}{2^{h+1}}+1 \leqslant c.\frac{n}{2^{h}}$$

$$\iff 1 \leqslant c.\frac{n}{2^{h}}-\frac{n}{2^{h+1}}$$

$$\iff 1 \leqslant \frac{n}{2^{h+1}}(2c-1)$$

$$\iff \frac{n}{2^{h+1}}\geqslant \frac{1}{2c-1} \ldots \tag 3$$

Now for (3) to comply with (2) we should have,

$$2.c-1 \geqslant 2 \iff c \geqslant \frac{3}{2}$$

Now is that single line in (1) worth this much effort or is it the situation that the step is trivial or intuitive that we can just mentally do the step. If it is the latter, please enlighten me with such intuition..

Even in this answer here that $$\frac{n}{2^{h+1}}\lt\frac{n}{2^{h}}$$ is intuitive but that $$1\lt\frac{n}{2^{h}}$$ is not quite intuitive and requires the use of (2) I feel

## 1 Answer

Since $$h \leq \lfloor \lg n \rfloor$$, we have $$2^h \leq n$$, and so $$n/2^{h+1} \geq 1/2$$. Therefore $$\left\lceil \frac{n}{2^{h+1}} \right\rceil \leq \frac{n}{2^{h+1}} + 1 = \frac{n}{2^{h+1}} + 2 \cdot \frac{1}{2} \leq \frac{n}{2^{h+1}} + 2 \frac{n}{2^{h+1}} = 3 \frac{n}{2^{h+1}}.$$ (In fact, if you are more careful then you can replace $$3$$ by $$2$$.)

More generally, if $$x \geq c > 0$$ then $$\lceil x \rceil = O(x)$$, where the hidden constant depends on $$c$$.

• Just wow!! Thanks a lot!! – Abhishek Ghosh Jun 21 at 13:34


text:
# Impossible equation to solve?

## Main Question or Discussion Point

Hi, I know its possible to get an answer by graphing the curves and finding the point of intersection but I was wondering if there was a way to do them algebraically.

sin(2x) = $$\frac{x}{2}$$

or $$e^{\frac{x}{8}}$$ = x

Also, do these types of equations have a name?

Nabeshin
Your first equation is not solvable (in terms of elementary functions or any I know of). The equation simply is not written in a way in which it is possible to express it as a solution x=something.

The second equation at first glance appears the same, but is actually solvable (although not in terms of elementary functions). The solution is:
x=-8 W(-1/8)
Where W is the Lambert W function. ( http://en.wikipedia.org/wiki/Lambert's_W_function )

I don't know of a name for these [unsolvable] equations, I'd call em non-algebraic (not sure if that's official though).

Last edited:
arildno
Homework Helper
Gold Member
Dearly Missed
They are called transcendental equations.

Thanks for the replies.

haha try this one. Let me know if you're interested in the problem, I actually got it from physicsforums.com.

$$\left [{1 \over 2}\sqrt{1 - n^2x^2} + {\arcsin (nx) \over 2n} \right ]_{0}^{6} = e + \pi$$

n=?

And what are the 0 and 6 ??

HallsofIvy
Homework Helper
I assume that he means that formula evaluated between 6 and 0: its value at 6 minus its value at 0 is equal to $e+ \pi$.

of course. Its an integral remember?

$$\int_0^{6}\sqrt{1 - (nx)^2}dx = e + \pi$$

I'm still in high school so is that possible to solve using my level of mathematics?

After I subbed the numbers in, I did a quick sketch on graphmatica and it didn't show any intersections between

$$y = \sqrt{1-36n^{2}} +\frac{arcsin (6n)}{n} -1$$

and y = 2e + 2pi

so have I done something wrong already?

I agree that there is no solution to

$$\left [{1 \over 2}\sqrt{1 - n^2x^2} + {\arcsin (nx) \over 2n} \right ]_{0}^{6} = e + \pi$$

However, there is a solution to

$$\int_0^{6}\sqrt{1 - (nx)^2}\,dx = e + \pi$$

camilus is mistaken in asserting that these are equal.

The equations in the first post can't be solved explicitly for x, but you could use a method of iteration to get as accurate a solution for x as you require.

I agree that there is no solution to

$$\left [{1 \over 2}\sqrt{1 - n^2x^2} + {\arcsin (nx) \over 2n} \right ]_{0}^{6} = e + \pi$$

However, there is a solution to

$$\int_0^{6}\sqrt{1 - (nx)^2}\dx = e + \pi$$

camilus is mistaken in asserting that these are equal.
wtf? explain..?

$$\int_0^{6}\sqrt{1 - (nx)^2}\dx = \left [{1 \over 2}\sqrt{1 - n^2x^2} + {\arcsin (nx) \over 2n} \right ]_{0}^{6} = e + \pi$$

now you gotta find what value of n will make will make the integral equal to e + pi. I have found n to several digits, although Im under the impression that n is nonalgebraic.

Mentallic
Homework Helper
camilus said:
wtf? explain..?
$$\int_0^{6}\sqrt{1 - (nx)^2}\dx \neq \left [{1 \over 2}\sqrt{1 - n^2x^2} + {\arcsin (nx) \over 2n} \right ]_{0}^{6}$$

Now, I can't actually explain because I don't know how to evaluate the integral, but I did go about it backwards and derived the result. They're not equal from what I can see.

the integral should be

$$\int \sqrt{1-(nx)^2}\,dx =\frac{1}{2}\;x\;\sqrt{1-(nx)^2} + \frac{1}{2n}\;\arcsin({nx)$$

notice the extra $$x$$?

uart
$$\int_0^{6}\sqrt{1 - (nx)^2}\dx \neq \left [{1 \over 2}\sqrt{1 - n^2x^2} + {\arcsin (nx) \over 2n} \right ]_{0}^{6}$$

Now, I can't actually explain because I don't know how to evaluate the integral, but I did go about it backwards and derived the result. They're not equal from what I can see.
It is relatively easy to show that:

$$\int \sqrt{1 - (nx)^2}\, dx = {1 \over 2} x \sqrt{1 - n^2x^2} + {\arcsin (nx) \over 2n}$$

Two methods come to mind.

Method 1.

Substitute $nx = \sin(u)[/tex] and it transforms into [itex]1/n \int \cos^2(u) du$. Then just use the trig identity cos^2(u) = 1/2 + 1/2 * cos(2u) and it's straight forward to get the above stated result.

Method 2. (A little more complicated but avoids need for trig identities and "trig of inverse trig" simplifications).

Note that $$\sqrt{1-(nx)^2} = 1/ \sqrt{1-(nx)^2} \, - \, (nx)^2 / \sqrt{1-(nx)^2}$$. The first term is pretty much a standard inverse sin integral and the second term is amenable to integration by parts. This is actually one of those integration by part problems where you end up with the original integral on both the left and right hand side of the equals sign and it simplifies down pretty easily (again to give the above stated result).

Edit. Yes thanks g_edgar. I didn't notice that missing x before.

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Mentallic
Homework Helper
No uart, you are wrong here. g_edgar posted the correct integral and I was able to confirm it for myself by again differentiating the result.

It is relatively easy to show that:...
Funny how it can be relatively easy to show the wrong answer :tongue:

uart
No uart, you are wrong here. g_edgar posted the correct integral and I was able to confirm it for myself by again differentiating the result.

Funny how it can be relatively easy to show the wrong answer :tongue:
Yes it's a relatively easy integral. I posted two ways to do it (and have done it many times in the past) but no I didn't actually do the calculations this time as the expression looked correct (as in it looked that same as what I've got in the past when I've actually done the integral rather than just describing the method to use). Sorry I didn't notice that the "x" was missing in the expression you posted.

Actually, the task is to solve for n

$$\sqrt{1-36n^{2}} +\frac{arcsin (6n)}{n} -\frac{1}{2}-\frac{arcsin(0)}{2n}= e+\pi$$

$$6n=sin(x)$$

$$n=\frac{sin(x)}{6}$$

$$\sqrt{1-sin^2(x)} + \frac{6x}{sin(x)} - \frac{1}{2} = e+ \pi$$

$$cos(x)+\frac{6x}{sin(x)}=e+\pi + \frac{1}{2}$$

uart
Actually, the task is to solve for n
Yes we knew that. :)

And with the corrected equation that would be,

$$3 \sqrt{1-36n^2} + {\frac {\sin^{-1}(6n)} {2n} = \pi + e$$

Which is still a transendental equation. (that is, no closed form solution in terms of standard functions). Numerically n=0.0617 to 3 significant figures.

Yes we knew that. :)

And with the corrected equation that would be,

$$3 \sqrt{1-36n^2} + {\frac {\sin^{-1}(6n)} {2n} = \pi + e$$

Which is still a transendental equation. (that is, no closed form solution in terms of standard functions). Numerically n=0.0617 to 3 significant figures.
Look at my way of solving, it's much easier. Yes, I know that it is still transcendental equation.

Mentallic
Homework Helper
Yes it's a relatively easy integral. I posted two ways to do it (and have done it many times in the past) but no I didn't actually do the calculations this time as the expression looked correct (as in it looked that same as what I've got in the past when I've actually done the integral rather than just describing the method to use). Sorry I didn't notice that the "x" was missing in the expression you posted.
Ahh ok, I see now. Your methods to solve them seemed unflawed, however since you insisted on the wrong answer, I wasn't sure what to think anymore


text:
Volume 301 - 35th International Cosmic Ray Conference (ICRC2017) - Session Cosmic-Ray Indirect. CRI- theory
Magnetic field damping in the Vela Jr. SNR
I. Sushch,* R. Brose, M. Pohl
*corresponding author
Full text: pdf
Pre-published on: August 16, 2017
Published on: August 03, 2018
Abstract
Vela Jr. (RX J0852.0$-$4622) is one of just a few known supernova remnants (SNRs) with the resolved shell across the whole electromagnetic spectrum from radio to very-high-energy (>100 GeV; VHE) gamma-rays. Its proximity and large size allow for detailed spatially resolved observations of the source making Vela Jr. one of the primary sources used for the study of particle acceleration and emission mechanisms in SNRs. High-resolution X-ray observations reveal steepening of the spectrum towards the interior of the remnant. In this study we aim for the self-consistent radiation model of Vela Jr. which at the same time would explain the broadband emission from the source and its spatially-dependent features. We solve the full particle transport equation combined with the high-resolution 1D hydrodynamic simulations (using Pluto code) and subsequently calculate the radiation from the remnant. We show that accounting for the damping of strong magnetic turbulence downstream of the forward shock might explain the observed radial dependence of the X-ray spectrum.
DOI: https://doi.org/10.22323/1.301.0580
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