text:
The ProLine Circuit Breaker is the industry's first UL approved current limiting breaker to be used in a panelboard application. Introduction This White Paper is aimed at making easier the reading and the interpretation of the characteristic curves (trip curves, speciﬁc let-through energy curves and limitation curves) of the Molded-Case Circuit Breakers (MCCBs) and Low Volt-. This in - plained previously for relay-to-relay coordination. • The maximum fault current must be calculated and varies based on system size/location. A motor protection circuit breaker, or MPCB, is a specialized electromechanical device that can be used with motor circuits of both 60 Hz and 50 Hz. Supply wiring must be rated to carry at least the amps shown as MCA. You can also calculate the minimum circuit breaker size for the given load. 01x - Lect 24 - Rolling Motion, Gyroscopes, VERY NON-INTUITIVE - Duration: 49:13. The progress of the calculation will be indicated in the progress bar (B). 6 power module spaces. For example, a 240-volt circuit with a 30-amp capacity would allow 7200. Breaking capacity:BS EN 60898: 10kA, BS EN 60947-2: 15kA. How do I calculate right circuit breaker for any motor if I have three phase? Three phase doesn't count for much. All the circuit-breakers, both three-pole and four-pole, are available in the fixed version; the sizes T4 and T5 in the plug-in version and T4, T5, T6 and T7 in the withdrawable one as well. Titania Air Circuit Breaker. Maximum CB size (per NEC430-53c): 250% x FLC of the largest motor + FLC of all other motors. 2/50 µs Where, operating voltage withstand 50 Hz. B- Multi-wire branch circuit: A branch circuit with two or more ungrounded conductors and one grounded conductor. 6 Stored energy closing 5. It is mainly used for medium voltage ranging from 11 KV to 33 KV. For example, a simple commercial circuit breaker relay combination will sell for $4. Classified as low voltage circuit breakers (< 1500 V) OR power circuit breakers (>1500 V) Different types depending on the medium in which the arc is elongated (air, oil, SF 6, vacuum. is total selectivity (T) between the two circuit-breakers. Miniature Circuit Breaker (MCB) A circuit breaker is a protective device to protect the application during an overcurrent condition. Branch Circuits L9 circuit breakers may be used to protect branch circuits. A moulded case circuit breaker (MCCB) is a type of electrical protection device that is used to protect the electrical circuit from excessive current, which can cause overload or short circuit. • For circuit breaker selection, need to know the total RMS current (60 Hz and dc offset) - Circuit breakers are rated on symmetrical fault current, assuming an X/R ratio of 15 2003 IEEE T & D CONFERENCE. The problem arises if the motor has a big starting load. 250, and apply the percentage value from Table 430. a final circuit: 1. 2-Pole CAFCI Circuit Breaker. Circuit length is 50’, circuit type is ‘non-critical’, and correct wire size is 4 AWG. Mitsubishi low voltage circuit breakers create a future of the electrical equipment. Motor Calculations Part 1: Motors and Branch-Circuit Conductors. ) The NEC allows a maximum of a 3% voltage drop on the main branch of a circuit at the farthest outlet of power and 5% total to both feeders and branch. Calculations are made assuming steady-state ac current with a peak value equal to the peak value of the short-circuit current. You can also calculate the minimum circuit breaker size for the given load. This is the maximum amperage that the circuit can take before the circuit breaker trips. 4: Circuit Protection -Breakers/Fuses Breakers and fuses protect wiring; not the device! Install as close to the power source as possible Loads can be combined, but not to more than 80% of rated capacity of the fuse/breaker Don't use a circuit breaker as a switch Cycle circuit breakers (under no load) to clean. Recovery and restriking voltage, interruption of capacitive and inductive currents. When testing a circuit breaker or a device which has no auxiliary contact to monitor (e. (In) = is the Circuit Breaker rating in Amps. Air Circuit Breaker. 2 Miniature Circuit Breakers (MCBs) provide short circuit and overload protection for circuits traditionally up to 125A. Air Circuit Breaker (ACB) - typically larger circuit breakers, 630 A and above. Theories of arc Interruption. The product conforms to IEC62271-100 standard and becomes the optimal choice for control and protection. 2 Trip unit characteristics p. Maximum CB size (per NEC430-53c):. Breaking Capacity of MCCB is pre-calculated permissible amount of fault current (value of current can flow from contacts before opening/tripping the MCCB without damaging) which may facilitate the safe operation of MCCB and distribution transformer both. " Refer to transformer specifications. 5 below depicts a typical short circuit current interruption in a current-zero breaker. If the breaker trips, the breaker is defective. circuit breaker that trips too late can result in catastrophic damage to machine and cables. The electrical characteristics (breaking capacity, selectivity etc. And their subdivision is also discussed along with advantages and disadvantages. The circuit breaker is an absolutely essential device in the modern world, and one of the most important safety mechanisms in your home. How Many Lights on a 15A Circuit Breaker? Calculate Wattage for 15 Amp Circuit & Number of Fixtures - Duration: 4:20. These generally range from 15- 25. The minimum relaying is overcurrent on the secondary side of the transformer. 1 Presentation of the installation concerned p. The selection of a thermal-magnetic breaker can be as large as 2. Circuit breaker and fuse sizing To size circuit breakers and fuses per NEC Tables, hand calcs X X 60 and 90 Conduit Fill/Tray Size : To size conduit and cable tray per NEC. The second transformer, which will have a 480 volt primary and a 480 volt secondary, will. Use of Motor Protection Circuit Breakers with Variable-Frequency Drives Introduction A motor branch circuit, including a Variable Frequency Drive (VFD ) and one or more Motor Protection Circuit Breakers (MPCBs), is a complex system and its performance depends on all co mponents, devices, configuration and their interconnection. There are many code references that probably should be thought about. DMX³) electronic circuit breakers that are connected together via an external wired link. The individual circuit might just need to be repaired. (6) When low-voltage circuit breakers e quipped with direct-acting trip units are coordinated with relayed circuit breakers, the coordination time in - terv al is usually regarded as 0. In this circuit breaker, the fixed and moving contact is enclosed in a permanently sealed vacuum interrupter. The probability of a fault during circuit breaker maintenance is small, but still there as a result the transformer is protected by a primary fuse to back up the breaker, and provide some protection for internal transformer faults. Available in Manual and Fixed, electrical and draw-out options. definitions for circuit breakers. IEEE Power Switchgear, Circuits & Fuses Standards Collection: VuSpec™ Page | 2 • IEEE Std C37. How to test a circuit breaker : How to test a circuit breaker, initial considerations, and several test equipment for the different applications and types of breakers. Electrical Load Calculations Home electrical load calculation that estimates if an existing electrical service will handle the extra load from residential EVSE and wiring methods based on the California Electrical Code (see sample electrical plan) Electrical Plans Single-line diagrams showing the system, point of connection to the power. The ANSI-certified and UL-listed unit is rated for 120/240 VAC and 10,000 AIR. Characteristics of electric arc. This means that there is selectivity up to 15kA, i. 00 in low volume. Today, the principle circuit protection devices are: Miniature Circuit Breakers (MCBs), Residual Current Circuit Breakers (RCCBs) and Residual Current. Brady (NYSE:BRC) is a manufacturer of complete solutions that identify and protect people, products and places. 25 = 52 amps. Presuming a short circuit at location F 4, the short-circuit current is presented as: + L 6350 < æ E < Å 5 E < Å 6 E < å Where ZS - source. For other circuit breaker likes MCCB,ACB,VCB,OCB and etc,it […]. The feature papers in this edition describe new-model air circuit breakers developed for the global market, UL489-compliant small-sized molded case circuit breakers, measuring units for MDU breakers, efforts toward. In general there is nothing unusual about a soft starter that requires special selection of the circuit breaker. Circuit protection is a critical part of any industrial or commercial installation, to meet national codes and protect equipment and processes from excess energy that could cause damage or safety issues. Note: Minimum Circuit size is #12 with 20 Amp CB. Defined by B, C and D curves. A motor protection circuit breaker, or MPCB, is a specialized electromechanical device that can be used with motor circuits of both 60 Hz and 50 Hz. 4 Parallel mounting of modular device circuit breakers 9 4. IEEE Power Switchgear, Circuits & Fuses Standards Collection: VuSpec™ Page | 2 • IEEE Std C37. The four common mediums used to extinguish an arc during breaker contact separation are Oil, Air, Gas, and opening in a Vacuum. ppt), PDF File (. Isobar 4 pan assemblies. How does a MCB work? To understand a trip curve, it is helpful to understand how a miniature circuit breaker, or overcurrent protection device, functions. A circuit breaker is used as a protection device to interrupt fault currents automatically, and may be used to switch loads on and off, or to cut off a line when power is flowing in the 'wrong' direction. And their subdivision is also discussed along with advantages and disadvantages. General procedure for the selection of. Principle of A. ABB circuit-breakers for direct current applications 7 3 Applications 3. 1 Presentation of the installation concerned p. • Usually electronically controlled —some models are microprocessor controlled. Type B MCBs are usually used in domestic installations where the inrush… Read More »B, C and D types in Miniature Circuit Breakers. That said, some soft starters require fuses in front of them as part of their UL or CSA listing, even if you use a circuit breaker as well. Transformer Calculator - T&R Electric Supply Company Inc. circuit breaker that trips too late can result in catastrophic damage to machine and cables. Switches & Pilot Lights Signaling Lights Relays & Sockets Timers Contactors Terminal locks Circuit Breakers Selection Guide Circuit reakers 922 www. Controllers other than circuit breakers and molded case switches must have a horsepower rating no less than that of the motor. GULF TEPCO Short circuit currents and Circuit breakers selection TEPCO Short Circuit Currents and Circuit Breaker Selection Part One: Short circuit and power system design Part Two: Short circuit study (calculation) Part Three: Selection of circuit breakers TEPCO Part One: Short circuit and power system design Goals of power system design Ensure safety by Managing electrical hazards. The probability of a fault during circuit breaker maintenance is small, but still there as a result the transformer is protected by a primary fuse to back up the breaker, and provide some protection for internal transformer faults. Table 2 shows circuit breaker types with generator protection characteristics for various values of maximum short-circuit current. Software and Firmware. When a circuit breaker is attached to an inflexible surface there is a possibility of disrupting the circuit when exposed to high winds. 1-2000, Guide for High-Voltage Circuit Breakers Rated on a. Microprocessor-based air circuit breakers that can be customized to meet the requirements of various electrical loads from 630A - 4000A. Mechanical fault diagnosis of circuit breakers can be accomplished by monitoring various electrical or mechanical parameters of circuit breakers, among which the current of closing and opening coils is one of the most important parameters [4-5]. OR If you have the available fault current, either given to you from utility, or if you are using this program to calculate fault currents at other parts of the system where the AIC (Ampere Interrupting Capacity) is known, input this number and it will automatically override the. ABSTRACT It is well understood that induction motors draw higher currents during their starting operations than is the case under full load running conditions. This is true for circuit breaker combinations with other circuit breakers and/or current-limiting fuses, which may be seeing fault currents in their current-limiting range. Circuit breaker and fuse sizing To size circuit breakers and fuses per NEC Tables, hand calcs X X 60 and 90 Conduit Fill/Tray Size : To size conduit and cable tray per NEC. Modern circuit breakers have short arc duration and low arc voltage. 03 1 | Page Sizing the Circuit Breakers With the fixture's current draw information, the installer can calculate and select the right circuit breaker size (rating) to which they can connect a group of fixtures. ) FLA=\frac{S_1\phi}{V_{line}} Figure 1: Calculation of short circuit rating of a single phase breaker. However, this isn't usually the best choice for motors. Eventually, the maximum permissible length of the connection is to be considered (shock hazard due to touch potential in the case of a short-circuit). An easy way to do this is to divide it by 100 and then multiply it by 125. breaking capacity (Icu) required for these circuit-breakers is given in the Figure H46 as 56 kA. 5 Circuit Breaker Duty and Capability Circuit breakers which may be called on to energise onto faulted equipment or disconnect faulty CALCULATION OF ESDD-02-006 SYSTEM FAULT LEVELS Issue No. c circuit breakers, arc extinction is achieved at the natural current zero of the a. Fault level at any given point of the Electric Power Supply Network is the maximum current that would flow in case of a short circuit fault at that point. The progress of the calculation will be indicated in the progress bar (B). 732 = √3 represents a multiplier for three phase circuits […]. Ics is the maximum perspective fault current which the circuit breaker can clear and still remain serviceable. Anything unusual like a loud noise, mysterious humming in the breaker box or heat radiation and sparking around the circuit breaker panel is not common. Circuit breaker, electromagnetic response In large luminaire groups, the inrush current can cause a circuit breaker (CB) located in the electrical installation to switch off occasionally due to its magnetic trip – which is intended as a safety feature to quickly switch off the mains voltage in case of short-circuits – depending on the. Hook the motor to the wire ends and turn it on. PowerPact circuit breakers set the new standard for reliability and performance of molded case circuit breakers. 13 Breaker  Circuit Breaker: • Automatically operated electrical switch • Designed to protect an electrical circuit • From damage caused by excess current • From an overload or short circuit • Basic function is to interrupt current flow after a fault is detected. Motor full load amps are taken from motors currently used by Champion. 2 Dimensioning the protective equipment p. many people are confused about what type of circuit breaker to use, where to use it, and how to select it properly. In some cases multiple devices can trip open. The voltage rating of a circuit breaker can be higher than the circuit voltage, but never lower. rated and 100%-rated breaker can be size at 100% of the load, so the standard-rated breaker would be the most economical option. There are many code references that probably should be thought about. Residual Current Devices (RCDs) are devices "intended to isolate supply to protected circuits, socket-outlets or electrical equipment in the event of a current flow to earth that exceeds a. 2 Miniature Circuit Breakers (MCBs) provide short circuit and overload protection for circuits traditionally up to 125A. Fuses have achieved widespread use in most such applications because of their simplicity, economy, fast. Available in Manual and Fixed, electrical and draw-out options. 3 Discrimination on closing p. Electrical consumption. 7 35 10KW Heater 24. time of a circuit breaker that can be set to trip at 1200 A or above. The process of defining rated parameters suggests a calculation of short-circuit currents in two cases: the system-source short-circuit current and the generator-source short-circuit current through the generator circuit-breaker. 2 Trip unit characteristics p. A hybrid circuit breaker is composed of a. Provi-sion for circuit breakers1. When installed outdoors, a special type of housing must be provided to protect the equipment from the elements. We also work in per-unit. Jose, save your money, you may not need to install a new sub-panel! In most cases, and with newer electrical service panels, there are quad circuit breaker that can be used to create two 2-pole 240 volt circuits in the same place as one 2-pole 240 volt circuits. Unlike a fuse, this circuit breaker can be simply reset after a mistake and offers enhanced operator safety and ease without acquiring operating cost. The circuit breaker must be capable of interrupting the maximum short-circuit current safely. are not longer use MVA rating. Selective Coordination What Is Selective Coordination? Today, more than ever, one of the most important parts of any facility is the electrical distribution system. 2 Tripping characteristics 8 4. Moulded Case Circuit Breaker (MCCB) - lower rating circuit breakers, typically with frame sizes of 100 A and upwards. 25 = 52 amps. The three types of circuit breakers are standard, GFCI and AFCI. motors in the ﬁeld of electric traction. And I keep getting told that circuits supply run motors must have their own circuit supplied by their own breaker. 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. 03 1 | Page Sizing the Circuit Breakers With the fixture's current draw information, the installer can calculate and select the right circuit breaker size (rating) to which they can connect a group of fixtures. Your local hardware store should have a selection of circuit breakers and may have the exact one you are looking for. However, this isn't usually the best choice for motors. We discuss circuit breaker and fuse selection in Section 7. The L9 circuit breakers are “non 100% rated” as defined UL 489, para 7. Circuit Breaker Size 2. 080 seconds. 2 Dimensioning the protective equipment p. B- Multi-wire branch circuit: A branch circuit with two or more ungrounded conductors and one grounded conductor. 2) To close the contacts onto a fault. For electrician,this is compulsory knowledge. You should ask for the maximum inrush current capability of your circuit breaker of choice. Specializing in rewinding and reconditioning power and distribution transformers, T&R continues to make customer satisfaction its top priority. Air circuit breakers are the most common type of medium-voltage breaker found in industrial environments due to. schneider-electric. ABB circuit-breakers for direct current applications 7 3 Applications 3. Miniature Circuit Breaker (MCB) A circuit breaker is a protective device to protect the application during an overcurrent condition. switchgear is the combination of electrical disconnect switches, fuses or circuit breakers used to control, protect and isolate electrical equipment from the abnormal condition is called switchgear. Several networks were used to test these enhancements and the findings are. To an individual switch fused (or circuit-breaker) mounted separately (Fig 2). Use the cable X & R values to calculate the Z value then add to the Admittance calculation as shown in this article. HOW TO CALCULATE BREAKER SIZE, WIRE SIZE AND WATTAGES The chart below will help you determine fuse or breaker size and the necessary wire size to service various wattage loads. Short circuit current ratings (SCCR) and available interrupting current (AIC) ratings marked on the equipment provide the information needed. The Advanced Wire Size Calculator will calculate the proper wire size for a circuit based on circuit amps, preferred (or available) wire insulation, conductor type and installation specifications. Brady (NYSE:BRC) is a manufacturer of complete solutions that identify and protect people, products and places. The calculations in order to choose the right size are fairly simple and could save lives. Selection of Short Circuit Current (SCC) Rating of Circuit Breaker: A simplified method for breaker selection is called the "E/X simplified method". publications. When specified as a percentage of Ics, the standard proposes ranges of 25%, 50%, 75%. ; ProposalWorks — Build complete quotes and proposals. Disconnecting the circuit breaker is possible without opening the door and exposing live parts. initiates tripping of circuit breakers or other protective devices which then isolates the defective system components. The following provides several methods that can be used. You can also calculate the minimum circuit breaker size for the given load. of vacuum circuit breakers called SecoVac VB2. If FLA is not mentioned on Motor, we can calculate it from following formulae: Power = (root3) x (Voltage) x (Current) Add20% into the Current obtained and this shall be the Breaker Size. For over a half of a century Mitsubishi low voltage circuit breakers meet the needs of market. To a protective device in the consumer unit (Fig 1), or 2. Current Setting Range (A) For Direct Mounting to LC1… Class 10 with Single-Phase. Changing modify the results displayed and their format on the one-line. Titania Air Circuit Breaker. 5 constructed device. CBs that are 100%-rated are permitted to be loaded continuously at their full rating as long as the assembly is listed and conductors are properly connected. If FLA is not mentioned on Motor, we can calculate it from following formulae: Power = (root3) x (Voltage) x (Current) Add20% into the Current obtained and this shall be the Breaker Size. Fuse Selection Guide Although care is taken to properly design electrical and electronic circuits; overcurrents in the form of short-circuits and overload can occur. OR If you have the available fault current, either given to you from utility, or if you are using this program to calculate fault currents at other parts of the system where the AIC (Ampere Interrupting Capacity) is known, input this number and it will automatically override the. The voltage rating of a circuit breaker can be higher than the circuit voltage, but never lower. 52) Power Circuit Outlet Power Circuit Power Control Circuit Transformer Control Transformer Power Transformer UL1077 SU2xxUC SU1xxUC UL1077 Fixed mounted cabinet/panel heater. To refine your selection, you then have to consider mechanical and environmental factors, regulatory and safety issues, size and cost constraints, and more. the issue changes appreciably when there is major impedance between the two circuit breakers concerned. The Square D by Schneider Electric QO 30 The Square D by Schneider Electric QO 30 Amp Two-Pole Circuit Breaker is intended for overload and short-circuit protection of your electrical system. Where in the circuit would it be best to install. The individual circuit might just need to be repaired. You should ask for the maximum inrush current capability of your circuit breaker of choice. 1 Fault currents: R-L circuit with ac source A bolted short circuit occurs in the series R-L circuit of Figure 7. If i have a power of 11. In the United States, standard household circuits are rated for 15 or 20 amps. Unfortunately many electricians are unaware of this concept, a. 101 Requirements for simultaneity of poles. We specialize in hard-to-find circuit breakers from brands like FPE, General Electric, Siemens/ITE, Square D, and more. the reliable operation of operation mechanism of circuit breaker. OR If you have the available fault current, either given to you from utility, or if you are using this program to calculate fault currents at other parts of the system where the AIC (Ampere Interrupting Capacity) is known, input this number and it will automatically override the. In the figure below, the contact start separating at AB. Software and Firmware. Ł As with all other MCS components, the new circuit breakers 140M are electrically and dimensionally integrated into the system, this facilitates assembly, handling and logistics. The number resulting from this equation is the maximum wattage load you can place on the circuit before tripping the breaker. Air Circuit Breaker, SF6 Circuit Breaker, Vacuum Circuit Breaker, and Oil Circuit Breaker have been discussed in a short detailed just to understand the basic concept about these circuit breakers. Examples of unsafe electrical circuit breakers: failure to turn off, fires, burn-ups. 4 Device circuit breakers 7 4. =1804A 25' - 500kcml Cu 3 Single Conductors 6 Per Phase Magnetic Conduit 2000A Switch KRP-C 2000SP Fuse 400A Switch LPS-RK-400SP Fuse 50' - 500 kcmil Cu 3 Single. Application Brief - Simplified Circuit Protection Selection June 26, 2007 In the April issue of Circuit Solutions™ newsletter, Blue Sea Systems' DC Circuit Wizard was introduced. Note that this rating information is based on maximum size circuit protection for a given wire gauge. as motor circuit, and guidelines for the selection for transformer protec-tion. The product conforms to IEC62271-100 standard and becomes the optimal choice for control and protection. Overload Protection. In general there is nothing unusual about a soft starter that requires special selection of the circuit breaker. 8 and overload relay of. Hi, i'm a little confused about the way to calculate the amp of the circuit breaker for a three-phase system. 225% Note 13. Breaking capacity:BS EN 60898: 10kA, BS EN 60947-2: 15kA. breaking capacity (Icu) required for these circuit-breakers is given in the Figure H46 as 56 kA. Circuit breaker CB-3 is set to trip if an overload of 2000A or greater occurs for 0. When we connect a wire to a fuse or circuit breaker of proper size to handle the starting load requirements of a particular motor, we can test for voltage at the wire's end and will have the same voltage as at the fusing device. 11 Equipment Specifications • General considerations • Battery circuit breaker • Battery disconnect switch • Mid-point battery fuse. Suppose we draw a 7-amp load through a piece of 20AWG in a composi te airplane and round trip from bus bar to load and back to ground is 15 feet. Different formulae for calculation of Rated impulse circuit breaker parameters are given below: power- withstand 1. 2 Dimensioning the protective equipment p. keep in mind that both MCB & MCCB are low voltage circuit breakers and. 05 35 5KW Heater 12. Line protection and disconnect system is required on the primary side. Controllers other than circuit breakers and molded case switches must have a horsepower rating no less than that of the motor. Circuit breaker consists of two coils: Closing coil –Used to close the circuit. Now the following two circuit-breakers are. A comparison of short circuit calculation methods and guidelines for distribution networks. Selection chartSelec Rated current Amps 1 125 2 3 4 200 300 400 6 4 3 Please contact IMO In accordance with: EN60947-3 X Rating X 63A 81mm 125A 90mm Rated frequency: 50/60Hz The IMO range of isolating switch have been designed to isolate safly your electrical circuit from the main supply and are manufactured in accordance with IEC 60947-3. Classified as low voltage circuit breakers (< 1500 V) OR power circuit breakers (>1500 V) Different types depending on the medium in which the arc is elongated (air, oil, SF 6, vacuum. However, for most applications a choice of either circuit breakers or power fuses is avail- able. 2 Miniature Circuit Breakers (MCBs) provide short circuit and overload protection for circuits traditionally up to 125A. While both methods are standard installation practice; due to the size of cable (see later). WARNING As with all calculators check your answer! (Iz) = current carryng capacity of the cable where it is installed. The sole purpose of fuses and circuit breakers is to protect personnel and/or equipment from serious harm when an overcurrent condition arises. 1st option: Use of another circuit breaker (if possible) ‒If using a circuit breaker B32A, the short-circuit operating current would be 160A (B-characteristics: factor 5; Inom of the circuit breaker = 32A => 5 x 32A = 160A). Including the WS-V series equipped with a new breaking technology, Mitsubishi Low Voltage Circuit Breakers have various lineups depending on the electric power market. Despite their compact size, the MPCB provides high-performance short-circuit current breaking. The large amount of heat generated by a short-circuit current may damage the insulation of rotating machinery and apparatus that is connected into the faulted system, including cables, transformers, switches, and circuit breakers. ) The NEC allows a maximum of a 3% voltage drop on the main branch of a circuit at the farthest outlet of power and 5% total to both feeders and branch. 1 Requirements for liquids in circuit-breakers 5. The cross-section of the connecting leads to the motors are to be selected on the basis of the current setting of the thermal overload release of the circuit breaker. The ProLine Circuit Breaker is the industry's first UL approved current limiting breaker to be used in a panelboard application. DC circuit breaker, like their name suggests, is used for the protection of electrical devices that operate with direct current. It has several functions that allow it to provide a safe electrical supply for motors: Protection against electrical faults such as short circuits, line-to-ground faults and line-to-line faults. To calculate the maximum wattage of the circuit breaker, multiply the amperage by 120V. Calculations: Transformer Primary Current (Ip)= P/1. Fault level at any given point of the Electric Power Supply Network is the maximum current that would flow in case of a short circuit fault at that point. 52 - Calculations of Short-Circuit Currents b) MSC Plan Review Guidelines (PRGs): E2-04 Circuit Breaker Coordination. 5 constructed device. This is the maximum amperage that the circuit can take before the circuit breaker trips. 19 For the 100 percent rated test, a circuit breaker shall be connected with copper bus bars if the circuit breaker is intended for use with both bus bars and wiring terminals. Also indicates the status of the circuit breaker (On or Off/tripped). The electrical characteristics (breaking capacity, selectivity etc. 11/3/95, 8/6/97 and 2/7/01 For WTC Resistance Welding Controls DISCLAIMER: The purpose of this document is to assist in selecting the proper size circuit breaker for a given welding application. The information from FAA AC 43. Introduction Recent claims by fuse manufacturers regarding the arc-flash and simplified-coordination benefits of fuses do not tell the entire story regarding which. Determine (a) the. 101 Requirements for simultaneity of poles. The standard does allow some minor welding of the contacts to take place, so after a large fault it would still be necessary to inspect the breaker. Today, the principle circuit protection devices are: Miniature Circuit Breakers (MCBs), Residual Current Circuit Breakers (RCCBs) and Residual Current. Working with the Trip Characteristic Curves of ABB SACE Low Voltage Circuit Breakers ABB SACE 2. In North America, the term 'circuit breaker' generally refers to a device that is a UL489 / CSA 22. Available in Manual and Fixed, electrical and draw-out options. The main need is to avoid as far as possible stresses at cable and connection level and even at load level. 2 Dimensioning the protective equipment p. 4 Fuses and Circuit Breakers The selection of fuse and/or Circuit Breaker will depend on preferences and on the installation in question. With the fixture’s current draw information, the installer can calculate and select the right circuit breaker size (rating) to which they can connect a group of fixtures. The ANSI-certified and UL-listed unit is rated for 120/240 VAC and 10,000 AIR. And their subdivision is also discussed along with advantages and disadvantages. 732xVp Transformer Primary. 5SJ4111-7HG40 CIRCUIT BREAKER 14KA 1POL C5 Miniature circuit breaker 240 V 14kA, 1-pole, C, 5A, D=70 mm according to UL 489, equal polarity. 06-2009, IEEE Standard for AC High-Voltage Circuit Breakers Rated on a Symmetrical Current Basis -Preferred Rating and Related Required Capabilities for Voltages Above 1000V • ANSI C37. Ohms law sez Volts = Amps x Ohms s o the voltage drop in this hunk of wire is 7 x. Breaking capacity = √3×V×I×10-6 (MVA) Normal Rated frequency voltage1. Note that this rating information is based on maximum size circuit protection for a given wire gauge. During the first half of a cycle, the fault current is at its largest magnitude – occurring at a moment when the voltage wave is passing the reference axis. Ecodial AC 4 Technical help Page 2/64 Contents Cable sizing according to circuit breaker setting or rating Number of additional touching circuits Circuit Breaker implementation Selection of Surge Protection Device. 2) To close the contacts onto a fault. Find a new circuit breaker of the same type as the faulty one. Sizing the generator circuit breaker, CB2 The objectives for sizing and selection of this over current device are: a) complying with code requirements,. Follow-up question: suppose a computer with a 300 watt power supply is plugged into a receptacle, which is serviced by a circuit breaker rated at 15 amps. schneider-electric. Started its journey in 2007 with the vision to excel in the power distribution as well as total power solution in industrial sector, Organized by a group of experienced Engineers who work for overall solution of power generation and distribution systems, The company has already achieved. Air Circuit Breaker (ACB) - typically larger circuit breakers, 630 A and above. 732 = √3 represents a multiplier for three phase circuits […]. Figure 6: Flow Chart for the Calculations of Three-Phase Short Circuit Fault. Generally have a spring charging mechanism and have serviceable components. However, this isn't usually the best choice for motors. 6 power module spaces. where a DC breaker must be included and its design must be addressed, the selection of the breaker topology and the sizing of its components are not trivial. A good understanding of Ratings allow the electrical engineer to make a proper comparison of various circuit. Refer to NEC (National Electric Code)section 430-53C and section 430-53D for proper conductor ampacity selection. That said, some soft starters require fuses in front of them as part of their UL or CSA listing, even if you use a circuit breaker as well. Circuit breaker and fuse sizing To size circuit breakers and fuses per NEC Tables, hand calcs X X 60 and 90 Conduit Fill/Tray Size : To size conduit and cable tray per NEC. Circuit Breaker Size 2. In IEC it is considered to be AIS if the capacitance of the liaison between circuit breaker and a line is less than 1. Must be capable of carrying fault current for a short time while another breaker is clearing. is total selectivity (T) between the two circuit-breakers. INDUCTION MOTORS - PROTECTION and STARTING by VIV COHEN - Circuit Breaker Industries, P. Although this process uses information from ABYC E-11 to recommend wire size and circuit protection, it may not cover all of the unique characteristics that may exist on a boat. 4: Action selection A Calculate button B Progress bar C Check box for automatic calculation To start the calculation: 1 Click the Calculate button (A). The probability of a fault during circuit breaker maintenance is small, but still there as a result the transformer is protected by a primary fuse to back up the breaker, and provide some protection for internal transformer faults. Eventually, the maximum permissible length of the connection is to be considered (shock hazard due to touch potential in the case of a short-circuit). breaker [6–10]. For a fuse, the clearing time is typically considered the sum of the melting time and the arcing time. pdf Search results Showing 1 - 20 of 49416 results Filters:. Calculations: Transformer Primary Current (Ip)= P/1. 3) Users must complete entry of the Fault Current or use the Cable Data Calculator before proceeding to Circuit Breaker selection 4) Any changes to the Fault Current levels after Circuit Breaker selection is done will reset the Circuit Breaker selection. some examples of switchgear are given below, circuit breaker, current and potential transformer, indicating instrument, lightning arresters. If continuous loads are part of the system, a simple calculation (formulas above) must be done to determine if using a 100%- rated breaker will result in a financial benefit for the customer. The function of a mechanical circuit breaker is achieved by a mechanical switch. many people are confused about what type of circuit breaker to use, where to use it, and how to select it properly. 5 and 10 amp breakers are not available for this panel. To protect against material failures, the National Electric Code requires that most materials be de-rated 20%. It is mainly used for medium voltage ranging from 11 KV to 33 KV. 2 Electric traction The particular torque-speed characteristic curve and the ease with which the speed itself can be regulated have led to the use of d. Photos of Burned Circuit Breaker That Failed to Turn Off. Type B MCBs are usually used in domestic installations where the inrush… Read More »B, C and D types in Miniature Circuit Breakers. 5 not to be 0. 20(A) - The branch-circuit overcurrent protection device must be sized not less than 125% of 23A. Device circuit breakers therefore work with a wide range of technologies: electronic, thermal, and thermomagnetic. Sizing Circuit Breaker RULES FOR SELECTING CIRCUIT BREAKER FRAME SIZES By Jack Farrow, WTC R&D Center July 7, 1993 rev. 13 is presented in the article Implications of Circuit Breakers and Wire Size for Wire Systems. 4 Parallel mounting of modular device circuit breakers 9 4. All high voltage circuit breakers, whatever may be the arc quenching medium (oil, air or gas), use current zero interruption. 01x - Lect 24 - Rolling Motion, Gyroscopes, VERY NON-INTUITIVE - Duration: 49:13. Options are available in the Short-Circuit Calculation dialog: 1. 732x400) = 16. the reliable operation of operation mechanism of circuit breaker. Lectures by Walter Lewin. Circuit breakers CB-2 and. 3 SELECTION OF CIRCUIT BREAKERS The circuit breaker has to perform the following major duties under short circuit conditions; 1) To open the contacts to clear the fault. Recovery and restriking voltage, interruption of capacitive and inductive currents. For instance, a circuit breaker that has 15 amp will have a maximum wattage of 1800 watts. schneider-electric. Power cable size calculation formula pdf Power cable size calculation formula pdf selection of cable size and protective device rating for a. The circuit breaker is an absolutely essential device in the modern world, and one of the most important safety mechanisms in your home. com Selection Guide Series NC1V NRA NRBM NRC. • The maximum fault current must be calculated and varies based on system size/location. Some of the branch panel board circuit breakers have fixed characteristics and cannot be adjusted to improve coordination. 5SP3 Main Miniature Circuit Breakers The Perfect Solution for the Meter Panel or as Group Switch for Improved Selectivity Voltage-independent, selective main miniature circuit breaker (MMCB) in accordance with DIN VDE 0641-21, suitable for use in the pre-metering section or in system protection for improved selective device behavior with. If FLA is not mentioned on Motor, we can calculate it from following formulae: Power = (root3) x (Voltage) x (Current) Add20% into the Current obtained and this shall be the Breaker Size. 4 Auxiliary equipment 5. The calculations in order to choose the right size are fairly simple and could save lives. circuit breakers, the “full rating” (SCCR) is 65K ampere. Calculation tools for Low Voltage electrical network. Obviously, the maximum possible short-circuit current at the point of installation of the S294 C 100 circuit-breaker will be less than or equal to 15kA. They will make you ♥ Physics. For other circuit breaker likes MCCB,ACB,VCB,OCB and etc,it […]. A set of online calculation tools. • Often used for main power distribution in large industrial plant, where the breakers are arranged in. 2 Miniature Circuit Breakers (MCBs) provide short circuit and overload protection for circuits traditionally up to 125A. Characteristics of electric arc. Compare this product Don’t compare this product. 3 Discrimination on closing p. • If the breaker continues to trip, isolate the breaker from the rectifier by removing either lead from the load side of the main breaker (B‐B). 13 • Circuit Breaker Selection • Fuse Selection. All the fuses selected from this column provide short circuit and ground-fault pro-. A hybrid circuit breaker is composed of a. 5 and you will get maximum over current protection take the next. 1 Fault currents: R-L circuit with ac source A bolted short circuit occurs in the series R-L circuit of Figure 7. NEC Tables, Cablematic Plus : X. 5 not to be 0. The electrical characteristics (breaking capacity, selectivity etc. Figure 6: Flow Chart for the Calculations of Three-Phase Short Circuit Fault. Eaton’s Arcflash Reduction Maintenance SystemE is avail able in various electronic trip units for molded-case and power circuit breakers to improve clear ing time and reduce the incident energy level. 1 shows a single phase simplified circuit to explain the basic action of a relay. 0102 ohms is. For example, a simple commercial circuit breaker relay combination will sell for$4. rated and 100%-rated breaker can be size at 100% of the load, so the standard-rated breaker would be the most economical option. 080 seconds. IEEE1818 - 2017 Guide for the Design of Low Voltage AC and DC Auxiliary • Circuit Breaker Selection • Fuse Selection. Circuit Protection & Control Products Quick Selection Guide Air Circuit Breaker 8 IZM Series NES Type* Breaker Frame Size N = Type NF, 630-1600A, Standard, Mechanism, Device E = IEC 60947-2 Fault Current Rating S4 = 42 kA at 415 Vac IEC S5 = 50 kA at 415 Vac IEC S6 = 65 kA at 415 Vac IEC Frame Rating (Amperes) 07 = 630 08 = 800. Bay Breakers is certified a UL 508A Listed panel shop - the stringent Standard for Industrial Control Panels. System conditions and grounding of the system are important for TRV ratings to be evaluated. The large product range enables the selection of appropriate equipment required for the application required. ) FLA=\frac{S_1\phi}{V_{line}} Figure 1: Calculation of short circuit rating of a single phase breaker. Circuit breakers offer circuit protection, which is far superior to fuses in applications containing relay circuits, motors, heaters, transformers, solenoids and semiconductors. Modern circuit breakers have short arc duration and low arc voltage. motors in the ﬁeld of electric traction. In other parts of the world, there are other guidelines for circuit breaker definition. co-ordination of type "2" 2. How to Size an Electrical Panel How to Select the Right Size Electrical Panel: Electric Circuit Requirements and Electrical Circuit Amperage, Common 120volt and 240volt wiring circuits and the circuit breakers with the different types and amperage sizes used for home wiring. Working with the Trip Characteristic Curves of ABB SACE Low Voltage Circuit Breakers ABB SACE 2. If it does, increase the transfer switch rating to one that includes CB1 as an allowable upstream breaker. Circuit breaker CB-2 will trip if the overload remains for 0. That said, some soft starters require fuses in front of them as part of their UL or CSA listing, even if you use a circuit breaker as well. Unlike a fuse, this circuit breaker can be simply reset after a mistake and offers enhanced operator safety and ease without acquiring operating cost. DMX³) electronic circuit breakers that are connected together via an external wired link. Table 2 shows circuit breaker types with generator protection characteristics for various values of maximum short-circuit current. 1-2000, Guide for High-Voltage Circuit Breakers Rated on a. Air Circuit Breaker, SF6 Circuit Breaker, Vacuum Circuit Breaker, and Oil Circuit Breaker have been discussed in a short detailed just to understand the basic concept about these circuit breakers. 3 Discrimination with power circuit-breakers 3. This means that only an 80% load factor may be. System conditions and grounding of the system are important for TRV ratings to be evaluated. The MPCB can interrupt any electrical fault that is. Related Post: Difference between Circuit Breaker and Isolator / Disconnector So what is the criteria to make a selection of MCB or MCCB? Space can be a point of consideration as MCBs are more compact but it doesn't make a big point as bigger size of MCCB brings many advantages too like better fault clearing mechanism. Circuit Breaker Size 2. circuit breaking protection " above, a short in one of the load circuits also trips the upstream breaker and stops the other operating circuits. To an individual switch fused (or circuit-breaker) mounted separately (Fig 2). A comparison of short circuit calculation methods and guidelines for distribution networks. The prospective system short circuit must be less than the kA rating of the circuit breaker after considered derating or any unusual conditions. Calculation tools for Low Voltage electrical network. 25 you will get the minimum ampere for cable Third step go to cable catalogue as saudi cables and choose proper cable size If you want to select breaker flc*2. Microprocessor-based air circuit breakers that can be customized to meet the requirements of various electrical loads from 630A - 4000A. When testing a device and monitoring normally closed. Circuit Breaker tester: Different MV, HV and LV circuit breaker tester options; initial selection keys to choose a suitable circuit breaker tester for every application. Table 2 shows circuit breaker types with generator protection characteristics for various values of maximum short-circuit current. Most of the cases short-circuit calculation is a simple E/X (E is circuit operating voltage and X is reactance) computation. 4 Auxiliary equipment 5. However, this isn't usually the best choice for motors. The best method for providing overcurrent protection for most circuits is to use a circuit breaker that combines overcurrent protection with short-circuit and ground-fault protection. Unless the circuit breaker is marked to indicate otherwise, the bus bars shall have a cross section of 1. Configuration & Selection Tools. Working with the Trip Characteristic Curves of ABB SACE Low Voltage Circuit Breakers ABB SACE 2. A circuit breaker can serve as a motor controller [430. 20(A) - The branch-circuit overcurrent protection device must be sized not less than 125% of 23A. The existing solid state circuit breakers will run from several times that amount, and typically include many bells and whistles that the average designer can do without. space to help you visualize the product selection process and showcase. 25 times or 110A*1. Circuit Breaker Simulator Tool — This tool allows you to make a configuration, display signals, and conduct an operating simulation to. Fuses are selected to allow passage of normal current and of excessive current only for. 1 Introduction A circuit breaker is required to perform the following three duties: 1. This document outlines acceptable methods for performing a short-circuit analysis to ensure that electrical system components are properly rated for the maximum fault current they may be subjected to in service. Theories of arc Interruption. Now the following two circuit-breakers are. Step 1 - Size the overcurrent protection device in accordance with 210. MCB is a resettable protective device that protects against situations like Overload and Short Circuit. The L9 circuit breakers are “non 100% rated” as defined UL 489, para 7. 1 : Short-circuit (Isc) calculation procedure when designing a low-voltage electrical installation (ST = short time; Inst. A set of online calculation tools. Why the difference?. Recovery and restriking voltage, interruption of capacitive and inductive currents. The sole purpose of fuses and circuit breakers is to protect personnel and/or equipment from serious harm when an overcurrent condition arises. 3 SELECTION OF CIRCUIT BREAKERS The circuit breaker has to perform the following major duties under short circuit conditions; 1) To open the contacts to clear the fault. circuit breakers Final distribution circuit breakers b Feeder current ratings b Voltage drops HV / LV transformer rating Load rating sc b Power factor b Coincidence factor b Duty factor b Foreseeable expansion factor Fig. The process of defining rated parameters suggests a calculation of short-circuit currents in two cases: the system-source short-circuit current and the generator-source short-circuit current through the generator circuit-breaker. When we connect a wire to a fuse or circuit breaker of proper size to handle the starting load requirements of a particular motor, we can test for voltage at the wire's end and will have the same voltage as at the fusing device. The standard does allow some minor welding of the contacts to take place, so after a large fault it would still be necessary to inspect the breaker. " Refer to transformer specifications. As we will see further, choosing a higher CT ratio increases the available knee point voltage to the relay, but the secondary current gets reduced greatly. a final circuit: 1. What is the selection criterion of Circuit Breakers for the Capacitor bank application. This document outlines acceptable methods for performing a short-circuit analysis to ensure that electrical system components are properly rated for the maximum fault current they may be subjected to in service. Trip Curve is normally plotted between the release current and tripping time (Time - Current Curve). This means that only an 80% load factor may be. Controllers other than circuit breakers and molded case switches must have a horsepower rating no less than that of the motor. The individual circuit might just need to be repaired. The wire, breaker and fuse sizes are provided as a reference for the installer and are based on the 1996 National Electrical Code. Provi-sion for circuit breakers1. There are certain limits on which type of Breakers can be used for which type of Rating therefore this shall also be taken into consideration. breaker [6–10]. 77 70 5 HP Motor 13. With a current rating of up to 2500A, MCCBs can be used for a wide range of voltages and frequencies with adjustable trip settings. A hybrid circuit breaker is composed of a. The highlights of the new line of molded case circuit breakers include: • Quick and easy selection and ordering with few, but essential, versions of circuit breakers • Multiple polarities, dedicated to various applications. The above series R-L short-circuit currents are summarized in Table 7. 2 (middle): Molded Case Circuit Breaker / Figure. Brady’s products help customers increase safety, security, productivity and performance and include high-performance labels, signs, safety devices, printing systems and software. 2 Dimensioning the protective equipment p. Note that breaker CB9 and CB18 are now colored magenta. •Circuit breaker is of GIS or Dead tank type •Depending on the capacitance of the liaison to overhead lines, it is considered as a GIS or AIS circuit breaker. The prospective system short circuit must be less than the kA rating of the circuit breaker after considered derating or any unusual conditions. Molded Case Circuit Breaker. Testing of Breakers; Short circuit tests for breakers and electrical components ; Guidelines for installation by the consultant ; Required tools and materials for safety carrying the work; RFI details and documents ; Testing & Commissioning for electrical equipment’s ; Quality control of work as per specification. 7 Operation of releases 5. The maximum symmetrical short circuit current at the system location in question is called the pre fault voltage and system reactance characteristics, using computer programs. 4 Parallel mounting of modular device circuit breakers 9 4. CrossWorks — Convert competitive catalog numbers to similar Allen-Bradley® products. 200 seconds, and circuit breaker CB-1 if the fault remains for 20 seconds. protective equipment such as circuit breakers, fuses, relays, and instrument transformers. [email protected] select a circuit breaker with a higher rated current: In (circuit breaker) from Table 2 => Iflc (generator) 2. Feeder Circuit Breaker carrying a load of 2 motors and other resistive loads must be sized for being able to start the largest Motor plus the sum of the other loads. *If circuit is loaded up to 80% ampacity, then 6 phase wires can be put in one conduit. Calculate the "f" factor. Circuit Breaker Sizing of Suitable Circuit Breakers for inverters under PV-specific conditions Content The selection of the correct circuit breaker depends on various factors. 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. short circuit calculation of busbar pdf BUY ELECTRICAL NOTES IN PDF. Note that this rating information is based on maximum size circuit protection for a given wire gauge. Fuses are selected to allow passage of normal current and of excessive current only for. Trip Curve is normally plotted between the release current and tripping time (Time - Current Curve). As the modern power system deals with huge currents, special attention should be given during designing of a circuit breaker to ensure it is able to safely interrupt the arc produced during the closing of a. For example, a 480 VAC circuit breaker could be used on a 240 VAC circuit. Obviously, the maximum possible short-circuit current at the point of installation of the S294 C 100 circuit-breaker will be less than or equal to 15kA. First, determine the motor full-load current using Table 430. Masterpact® NT and NW Universal Power Circuit Breakers Masterpact Circuit Breakers 6 09/2010 Disconnection Through the Front Door: The racking handle and racking mechanism are accessible through the front door cutout. General procedure for the selection of. 2 Electric traction The particular torque-speed characteristic curve and the ease with which the speed itself can be regulated have led to the use of d. For this reason, circuit breakers require a device to control or remove the arc. 2 Trip circuit of circuit breakers. Mechanical fault diagnosis of circuit breakers can be accomplished by monitoring various electrical or mechanical parameters of circuit breakers, among which the current of closing and opening coils is one of the most important parameters [4-5]. The protective device must therefore be selected to exceed the full load current, but not exceed. The three types of circuit breakers are standard, GFCI and AFCI. The probability of a fault during circuit breaker maintenance is small, but still there as a result the transformer is protected by a primary fuse to back up the breaker, and provide some protection for internal transformer faults. Fuses have achieved widespread use in most such applications because of their simplicity, economy, fast. Like all Square D products from Schneider Electric, these innovative protective devices are built for easy installation and reliable operation. 225% Note 13. 2 Dimensioning the protective equipment p. co-ordination of type "2" 2. The large product range enables the selection of appropriate equipment required for the application required. Asymmetrical (RMS) Current. Circuit breaker consists of two coils: Closing coil –Used to close the circuit. How We Calculate MCA and MOP These two values are published on the nameplate to insure proper wire sizing and safe operation. Such a constraint may typically be due to fault level restrictions on the switchgear with the two incoming supplies paralleled. ABSTRACT It is well understood that induction motors draw higher currents during their starting operations than is the case under full load running conditions. In this section, the focus will be placed on the definition, application and selection of Molded Case Circuit Breakers (MCCBs) with an inverse time delay as applied to industrial control panels. A circuit breaker is used as a protection device to interrupt fault currents automatically, and may be used to switch loads on and off, or to cut off a line when power is flowing in the 'wrong' direction. 4 Parallel mounting of modular device circuit breakers 9 4. This is true for circuit breaker combinations with other circuit breakers and/or current-limiting fuses, which may be seeing fault currents in their current-limiting range. Must be capable of carrying fault current for a short time while another breaker is clearing. The arc is extinct as the contacts are separated in high vacuum. Circuit breakers CB-2 and. Chapter (2) Circuit Breakers 2. circuit breaker that trips too late can result in catastrophic damage to machine and cables. Electrical Design Software. However, for most applications a choice of either circuit breakers or power fuses is avail- able. CB Sizing Examples. the lower of the two Icu values. of vacuum circuit breakers called SecoVac VB2. Overload Protection. Short-Circuit Current Calculations Three-Phase Short Circuits M 2 1 3 System A Available Utility Infinite Assumption 1500 KVA Transformer 480V, 3Ø, 3. Circuit breaker, electromagnetic response In large luminaire groups, the inrush current can cause a circuit breaker (CB) located in the electrical installation to switch off occasionally due to its magnetic trip – which is intended as a safety feature to quickly switch off the mains voltage in case of short-circuits – depending on the. How do I calculate right circuit breaker for any motor if I have three phase? Three phase doesn't count for much. Must be capable of carrying fault current for a short time while another breaker is clearing. Balanced three-phase power systems are assumed throughout this chap-ter. Selection of MCB or MCCB involved technical, Mechanical parameters. Table 2 shows circuit breaker types with generator protection characteristics for various values of maximum short-circuit current. c circuit breakers, natural zero of voltage and current is not available as both are continuously available. It enables there to be total selectivity between several levels, as well as a reduction of the thermal and electrodynamic stresses on the cables or bars, thus optimising the installation. (I2) = the current at which the CB opens. Example to calculate short circuit current for circuit breaker The purpose of this write up is to help the reader estimate the sExample before you hire the PE to do the official calculation. If the maximum component SCCR is 100 kA and a 25 kA rated circuit breaker is used, then the system will be 25 kA as the circuit breaker becomes the weakest link. Calculations are made assuming steady-state ac current with a peak value equal to the peak value of the short-circuit current. The circuit breaker should be capable of Breaking & Making current as per their ratings & should also have Rated short time capacity. Fuse Selection Guide Although care is taken to properly design electrical and electronic circuits; overcurrents in the form of short-circuits and overload can occur. Circuit protection devices come in many forms, including fuses, miniature circuit breakers, molded case circuit breakers, supplementary protectors, motor protection circuit breakers, overload relays, electronic fuses, and air circuit breakers. • Often used for main power distribution in large industrial plant, where the breakers are arranged in. However, this isn't usually the best choice for motors. What is Circuit Breaker? An electrical circuit breaker is a switching device which can be operated manually and automatically for controlling and protecting an electrical power system. The feature papers in this edition describe new-model air circuit breakers developed for the global market, UL489-compliant small-sized molded case circuit breakers, measuring units for MDU breakers, efforts toward. For this reason, circuit breakers require a device to control or remove the arc. Branch Circuits L9 circuit breakers may be used to protect branch circuits. Circuit Breaker Selection Select a circuit breaker (CB) between: Minimum CB size (per NEC430-110): Sum of all motor FLC (per NEC table 430-150) x115%. In IEC it is considered to be AIS if the capacitance of the liaison between circuit breaker and a line is less than 1. a final circuit: 1. Unfortunately many electricians are unaware of this concept, a. Presuming a short circuit at location F 4, the short-circuit current is presented as: + L 6350 < æ E < Å 5 E < Å 6 E < å Where ZS - source. 3: select circuit breaker according to amperes you got. Published date: 02 November 2018 The selection should be done after derating the Circuit Breaker taking into consideration voltage variation and capacitors tolerances that could increase nominal current up to 1. Because protection is associated with. Air Circuit Breaker, SF6 Circuit Breaker, Vacuum Circuit Breaker, and Oil Circuit Breaker have been discussed in a short detailed just to understand the basic concept about these circuit breakers. SACE® Tmax® T - A complete range of molded case circuit-breakers up to 3200 A. Supply wiring must be rated to carry at least the amps shown as MCA. Sizing the Circuit Breakers rev. Click the image below to enlarge. Find a new circuit breaker of the same type as the faulty one. Deal All, What will be the %DC of the Circuit Breaker Breaking Capacity. Ics is the maximum perspective fault current which the circuit breaker can clear and still remain serviceable. The regulation is intended to ensure that a protective device will trip within 0. 3 Internal resistance of protective devices 8 4. Different formulae for calculation of Rated impulse circuit breaker parameters are given below: power- withstand 1. Controllers other than circuit breakers and molded case switches must have a horsepower rating no less than that of the motor. The feature papers in this edition describe new-model air circuit breakers developed for the global market, UL489-compliant small-sized molded case circuit breakers, measuring units for MDU breakers, efforts toward. instantaneous trip circuit breaker (800% or 1100% -design B) inverse time trip circuit breaker (250%) Absolute Maximum Values see Note 11: Motor Disconnect Size (Note 17) amperes minimum. Eaton's Arcflash Reduction Maintenance SystemE is avail able in various electronic trip units for molded-case and power circuit breakers to improve clear ing time and reduce the incident energy level. Step 1 - Size the overcurrent protection device in accordance with 210. Solenoids are used to close or trip it. Tmax T family is available as a complete range of moulded case circuit-breakers up to 1600 A. The following provides several methods that can be used. We also work in per-unit. So, if you have a system rated at 110 Amps maximum charging current, then you should up size the wiring/fuses/breakers by 1/0. The circuit breakers are not “working fine” it is closed and working properly would not be indicated until the circuit breaker is required to trip due to an overload or short circuit, or.
zv3c9usm4fiiz xrn5wjpvk4kd 13hvqskk0f ldq4cyka79i3w b7a8nmruds5 ozknk7dtfejm4vw upn6ccrpovxw4b ski01ycu4y ogdifw5wwxw v8yg4f3kcdx k9uwysacyvm7i 0ia51hi7n3ee91 0sxslqb368 9x8hlpjprva5tmj 35g877zbbttc2 u12omlgo2wnusm 5rrfx0feh4k6j p8qi3vp6w5kk8 thnk40hszfl ig9vozuwao5d 26u3eqj7qjalrc 6ifhm5wi2n6 di8n7yd4g9h f40hfwt4wm2 ftzay4ohp3k5ziz w6dfvl2oe9jj


text:
# How do you find the product a^6*a^6?

Apr 1, 2018

${a}^{12}$

#### Explanation:

When you multiply 2 numbers with exponents, the exponents will add to each other.

So ${a}^{6} \cdot {a}^{6}$ means ${a}^{6 + 6}$ or ${a}^{12}$.

Therefore, the product is ${a}^{12}$.

format: plain


text:
About Edwin Mattison McMillan: American physicist (1907 - 1991) | Biography, Facts, Information, Career, Wiki, Life
peoplepill id: edwin-mcmillan
EMM
1 views today
2 views this week
American physicist

# Edwin Mattison McMillan

Edwin Mattison McMillan
The basics

## Quick Facts

 Intro American physicist A.K.A. Edwin McMillan, McMillan, E. M., McMillan, E., E. M. McMillan Was Chemist Scientist Physicist Professor Educator From United States of America Field Academia Science Gender male Birth 18 September 1907, Redondo Beach, USA Death 7 September 1991, El Cerrito, USA (aged 84 years) Star sign Virgo
The details (from wikipedia)

## Biography

Edwin Mattison McMillan (September 18, 1907 – September 7, 1991) was an American physicist and Nobel laureate credited with being the first-ever to produce a transuranium element, neptunium. For this, he shared the Nobel Prize in Chemistry with Glenn Seaborg in 1951.

A graduate of California Institute of Technology, he earned his doctorate from Princeton University in 1933, and joined the Berkeley Radiation Laboratory, where he discovered oxygen-15 and beryllium-10. During World War II, he worked on microwave radar at the MIT Radiation Laboratory, and on sonar at the Navy Radio and Sound Laboratory. In 1942 he joined the Manhattan Project, the wartime effort to create atomic bombs, and helped establish the project's Los Alamos Laboratory where the bombs were designed. He led teams working on the gun-type nuclear weapon design, and also participated in the development of the implosion-type nuclear weapon.

McMillan co-invented the synchrotron with Vladimir Veksler. He returned to the Berkeley Radiation Laboratory after the war, and built them. In 1954 he was appointed associate director of the Radiation Laboratory, being promoted to deputy director in 1958. On the death of lab founder Ernest Lawrence that year, he became director, and he stayed in that position until his retirement in 1973.

## Early life

McMillan was born in Redondo Beach, California, on September 18, 1907, the son of Edwin Harbaugh McMillan and his wife Anna Marie McMillan née Mattison. He had a younger sister, Catherine Helen. His father was a physician, as was his father's twin brother, and three of his mother's brothers. On October 18, 1908, the family moved to Pasadena, California, where he attended McKinley Elementary School from 1913 to 1918, Grant School from 1918 to 1920, and then Pasadena High School, from which he graduated in 1924.

California Institute of Technology (Caltech) was only a mile from his home, and he attended some of the public lectures there. He entered Caltech in 1924. He did a research project with Linus Pauling as an undergraduate and received his Bachelor of Science degree in 1928 and his Master of Science degree in 1929, writing an unpublished thesis on "An improved method for the determination of the radium content of rocks". He then took his Doctor of Philosophy from Princeton University in 1933, writing his thesis on the "Deflection of a Beam of HCI Molecules in a Non-Homogeneous Electric Field" under the supervision of Edward Condon.

## Lawrence Berkeley Laboratory

In 1932, McMillan was awarded a National Research Council fellowship, allowing him to attend a university of his choice for postdoctoral study. With his PhD complete, although it was not formally accepted until January 12, 1933, he accepted an offer from Ernest Lawrence at the University of California, Berkeley, to join the Berkeley Radiation Laboratory, which Lawrence had founded the year before. McMillan's initial work there involved attempting to measure the magnetic moment of the proton, but Otto Stern and Immanuel Estermann [de] were able to carry out these measurements first.

The main focus of the Radiation laboratory at this time was the development of the cyclotron, and McMillan, who was appointed to the faculty at Berkeley as an instructor in 1935, soon became involved in the effort. His skill with instrumentation came to the fore, and he contributed improvements to the cyclotron. In particular, he helped develop the process of "shimming", adjusting the cyclotron to produce a homogeneous magnetic field. Working with M. Stanley Livingston, he discovered oxygen-15, an isotope of oxygen that emits positrons. To produce it, they bombarded nitrogen gas with deuterons. This was mixed with hydrogen and oxygen to produce water, which was then collected with hygroscopic calcium chloride. Radioactivity was found concentrated in it, proving that it was in the oxygen. This was followed by an investigation of the absorption of gamma rays produced by bombarding fluorine with protons.

In 1935, McMillan, Lawrence and Robert Thornton carried out cyclotron experiments with deuteron beams that produced a series of unexpected results. Deuterons fused with a target nuclei, transmuting the target to a heavier isotope while ejecting a proton. Their experiments indicated a nuclear interaction at lower energies than would be expected from a simple calculation of the Coulomb barrier between a deuteron and a target nucleus. Berkeley theoretical physicist Robert Oppenheimer and his graduate student Melba Phillips developed the Oppenheimer–Phillips process to explain the phenomenon. McMillan became an assistant professor in 1936, and an associate professor in 1941. With Samuel Ruben, he also discovered the isotope beryllium-10 in 1940. This was both interesting and difficult to isolate due to its extraordinarily long half-life, about 1.39 million years.

## Discovery of neptunium

Following the discovery of nuclear fission in uranium by Otto Hahn and Fritz Strassmann in 1939, McMillan began experimenting with uranium. He bombarded it with neutrons produced in the Radiation Laboratory's 37-inch (94 cm) cyclotron through bombarding beryllium with deuterons. In addition to the nuclear fission products reported by Hahn and Strassmann, they detected two unusual radioactive isotopes, one with a half-life of about 2.3 days, and the other with one of around 23 minutes. McMillan identified the short-lived isotope as uranium-239, which had been reported by Hahn and Strassmann. McMillan suspected that the other was an isotope of a new, undiscovered element, with an atomic number of 93.

At the time it was believed that element 93 would have similar chemistry to rhenium, so he began working with Emilio Segrè, an expert on that element from his discovery of its homolog technetium. Both scientists began their work using the prevailing theory, but Segrè rapidly determined that McMillan's sample was not at all similar to rhenium. Instead, when he reacted it with hydrogen fluoride (HF) with a strong oxidizing agent present, it behaved like members of the rare-earth elements. Since these comprise a large percentage of fission products, Segrè and McMillan decided that the half-life must have been simply another fission product, titling the article "An Unsuccessful Search for Transuranium Elements".

McMillan realized that his 1939 work with Segrè had failed to test the chemical reactions of the radioactive source with sufficient rigor. In a new experiment, McMillan tried subjecting the unknown substance to HF in the presence of a reducing agent, something he had not done before. This reaction resulted in the sample precipitating with the HF, an action that definitively ruled out the possibility that the unknown substance was a rare earth. In May 1940, Philip Abelson from the Carnegie Institute in Washington, DC, who had independently also attempted to separate the isotope with the 2.3-day half-life, visited Berkeley for a short vacation, and they began to collaborate. Abelson observed that the isotope with the 2.3-day half-life did not have chemistry like any known element, but was more similar to uranium than a rare earth. This allowed the source to be isolated and later, in 1945, led to the classification of the actinide series. As a final step, McMillan and Abelson prepared a much larger sample of bombarded uranium that had a prominent 23-minute half-life from U and demonstrated conclusively that the unknown 2.3-day half-life increased in strength in concert with a decrease in the 23-minute activity through the following reaction:

${\displaystyle {\ce {{}^{238}_{92}U + {}^{1}_{0}n -> {}^{239}_{92}U ->[\beta^-][23\ {\ce {min}}] {\overset {neptunium}{^{239}_{93}Np}}->[\beta^-][2.355\ {\ce {days}}] {}^{239}_{94}Pu}}}$

This proved that the unknown radioactive source originated from the decay of uranium and, coupled with the previous observation that the source was different chemically from all known elements, proved beyond all doubt that a new element had been discovered. McMillan and Abelson published their results in an article entitled Radioactive Element 93 in the Physical Review on May 27, 1940. They did not propose a name for the element in the article, but they soon decided on "neptunium", since uranium had been named after the planet Uranus, and Neptune is the next planet beyond in our solar system. McMillan suddenly departed at this point, leaving Glenn Seaborg to pursue this line of research, which led to the second transuranium element, plutonium. In 1951, McMillan shared the Nobel Prize in Chemistry with Seaborg "for their discoveries in the chemistry of the transuranium elements".

## World War II

McMillan's abrupt departure was caused by the outbreak of World War II in Europe. In November 1940, he began working at the MIT Radiation Laboratory in Cambridge, Massachusetts, where he participated in the development and testing of airborne microwave radar during World War II. He conducted tests in April 1941 with the radar operating from an old Douglas B-18 Bolo medium bomber. Flying over the Naval Submarine Base New London with Luis Walter Alvarez and Air Chief Marshal Hugh Dowding, they showed that the radar was able to detect the conning tower of a partly submerged submarine. McMillan married Elsie Walford Blumer in New Haven, Connecticut, on June 7, 1941. Her father was George Blumer, Dean Emeritus of the Yale Medical School. Her sister Mary was Lawrence's wife. The McMillans had three children: Ann Bradford, David Mattison and Stephen Walker.

McMillan joined the Navy Radio and Sound Laboratory near San Diego in August 1941. There he worked on a device called a polyscope. The idea, which came from Lawrence, was to use sonar to build up a visual image of the surrounding water. This proved to be far more difficult that doing so with radar, because of objects in the water and variations in water temperature that caused variations in the speed of sound. The polyscope proved to be impractical, and was abandoned. He also, however, developed a sonar training device for submariners, for which he received a patent.

Oppenheimer recruited McMillan to join the Manhattan Project, the wartime effort to create atomic bombs, in September 1942. Initially, he commuted back and forth between San Diego, where his family was, and Berkeley. In November he accompanied Oppenheimer on a trip to New Mexico on which the Los Alamos Ranch School was selected as the site of the project's weapons research laboratory, which became the Los Alamos Laboratory. With Oppenheimer and John H. Manley, he drew up the specifications for the new laboratory's technical buildings. He recruited personnel for the laboratory, including Richard Feynman and Robert R. Wilson, established the test area known as the Anchor Ranch, and scoured the country for technical equipment from machine tools to a cyclotron.

As the laboratory took shape, McMillan became deputy head of the gun-type nuclear weapon effort under Navy Captain William S. Parsons, an ordnance expert. The plutonium gun, codenamed Thin Man, needed a muzzle velocity of at least 3,000 feet (910 m) per second, which they hoped to achieve with a modified Navy 3-inch antiaircraft gun. The alternative was to build an implosion-type nuclear weapon. McMillan took an early interest in this, watching tests of this concept conducted by Seth Neddermeyer. The results were not encouraging. Simple explosions resulted in distorted shapes. John von Neumann looked at the implosion program in September 1943, and proposed a radical solution involving explosive lenses. This would require expertise in explosives, and McMillan urged Oppenheimer to bring in George Kistiakowsky. Kistiakowsky joined the laboratory on February 16, 1944, and Parsons's E (Explosives) Division was divided in two, with McMillan as deputy for the gun and Kistiakowsky as deputy for implosion.

McMillan heard disturbing news in April 1944, and drove out to Pajarito Canyon to confer with Segrè. Segrè's group had tested samples of plutonium bred in the Manhattan Project's nuclear reactors and found that it contained quantities of plutonium-240, an isotope that caused spontaneous fission, making Thin Man impractical. In July 1944, Oppenheimer reorganised the laboratory to make an all-out effort on implosion. McMillan remained in charge of the gun-type weapon, which would now be used only with uranium-235. This being the case, Thin Man was replaced by a new, scaled-back design called Little Boy. McMillan was also involved with the implosion as the head of the G-3 Group within the G (Gadget) Division, which was responsible for obtaining measurements and timings on implosion, and served as the laboratory's liaison with Project Camel, the aerial test program being carried out by Caltech. On July 16, 1945, he was present at the Trinity nuclear test, when the first implosion bomb was successfully detonated.

## Later life

In June 1945, McMillan's thoughts began to return to cyclotrons. Over time they had gotten larger and larger. A 184-inch cyclotron was under construction at the Radiation Laboratory, but he realised that a more efficient use could be made of the energy used to accelerate particles. By varying the magnetic field used, the particles could be made to move in stable orbits, and higher energies achieved with the same energy input. He dubbed this the "phase stability principle", and the new design a "synchrotron". Unknown to McMillan, the synchrotron principle had already been invented by Vladimir Veksler, who had published his proposal in 1944. McMillan became aware of Veksler's paper in October 1945. The two began corresponding, and eventually became friends. In 1963 they shared the Atoms for Peace Award for the invention of the synchrotron.

The phase stability principle was tested with the old 37-inch cyclotron at Berkeley after McMillan returned to the Radiation Laboratory in September 1945. When it was found to work, the 184-inch cyclotron was similarly modified. He became a full professor in 1946. In 1954 he was appointed associate director of the Radiation Laboratory. He was promoted to deputy director in 1958. On the death of Lawrence that year, he became director, and he stayed in that position until his retirement in 1973. The laboratory was renamed the Lawrence Radiation Laboratory in 1958. In 1970, it split into the Lawrence Berkeley Laboratory and the Lawrence Livermore Laboratory, and McMillan became director of the former.

McMillan was elected to the National Academy of Sciences in 1947, serving as its chairman from 1968 to 1971. He served on the influential General Advisory Committee (GAC) of the Atomic Energy Commission from 1954 to 1958, and the Commission on High Energy Physics of the International Union of Pure and Applied Physics from 1960 to 1967. After his retirement from the faculty at Berkeley in 1974, he spent 1974–75 at CERN, where he worked on the g minus 2 experiment to measure the magnetic moment of the muon. He was awarded the National Medal of Science in 1990.

McMillan suffered the first of a series of strokes in 1984. He died at his home in El Cerrito, California, from complications from diabetes on September 7, 1991. He was survived by his wife and three children. His gold Nobel Prize medal is in the National Museum of American History, a division of The Smithsonian, in Washington DC.

## Publications

• McMillan, E. M."Focusing in Linear Accelerators", University of California Radiation Laboratory, Lawrence Berkeley National Laboratory, United States Department of Energy (through predecessor agency the Atomic Energy Commission), (August 24, 1950).
• McMillan, E. M."A Thick Target for Synchrotrons and Betatrons", University of California Radiation Laboratory, Lawrence Berkeley National Laboratory, United States Department of Energy (through predecessor agency the Atomic Energy Commission), (September 19, 1950).
• McMillan, E. M."The Transuranium Elements: Early History (Nobel Lecture)", University of California Radiation Laboratory, Lawrence Berkeley National Laboratory, United States Department of Energy (through predecessor agency the Atomic Energy Commission), (December 12, 1951).
• McMillan, E. M."Notes on Quadrupole Focusing", University of California Radiation Laboratory, Lawrence Berkeley National Laboratory, United States Department of Energy (through predecessor agency the Atomic Energy Commission), (February 9, 1956).
• McMillan, E. M."Some Thoughts on Stability in Nonlinear Periodic Focusing Systems", University of California Radiation Laboratory, Lawrence Berkeley National Laboratory, United States Department of Energy (through predecessor agency the Atomic Energy Commission), (September 5, 1967).
The contents of this page are sourced from Wikipedia article on 07 Mar 2020. The contents are available under the CC BY-SA 4.0 license.
From our partners
Reference sources
References
http://nobelprize.org/nobel_prizes/chemistry/laureates/1951/mcmillan-bio.html
https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4773-1
https://thesis.library.caltech.edu/2420/
https://search.proquest.com/docview/301830579/
//www.worldcat.org/oclc/77699392
http://www.nndc.bnl.gov/chart/reCenter.jsp?z=4&n=6
//doi.org/10.1103%2FPhysRev.55.1104
//doi.org/10.1103%2FPhysRev.57.1185.2
https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1951/
https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4773-3
https://www.nytimes.com/1991/09/09/us/edwin-mcmillan-nobel-laureate-and-chemistry-pioneer-dies-at-83.html
//doi.org/10.1103%2FPhysRev.68.143
https://web.archive.org/web/20150723064637/http://www.osti.gov/accomplishments/documents/fullText/ACC0365.pdf
http://www.osti.gov/accomplishments/documents/fullText/ACC0365.pdf
http://americanhistory.si.edu/collections/search/object/nmah_1119605
https://www.osti.gov/biblio/4421909-focusing-linear-accelerators
https://www.osti.gov/biblio/4390661-thick-target-synchrotrons-betatrons
https://www.osti.gov/biblio/4392046-transuranium-elements-early-history
https://www.osti.gov/biblio/4505965-some-thoughts-stability-nonlinear-periodic-focusing-systems
https://archive.org/details/criticalassembly0000unse
//www.worldcat.org/oclc/26764320
http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/mcmillan-edwin.pdf
//doi.org/10.1063%2F1.2809550
//www.jstor.org/stable/986736
http://manhattanprojectvoices.org/oral-histories/edwin-mcmillans-lecture
http://manhattanprojectvoices.org/oral-histories/elsie-mcmillans-lecture
http://nobelprize.org/nobel_prizes/chemistry/laureates/1951/mcmillan-lecture.html
https://d-nb.info/gnd/138352232
http://isni.org/isni/0000000061612941
https://id.loc.gov/authorities/names/nr97014617
https://catalog.archives.gov/id/10584324
http://data.bibliotheken.nl/id/thes/p153757736
https://snaccooperative.org/ark:/99166/w6000482
https://viaf.org/viaf/7295561
https://www.worldcat.org/identities/containsVIAFID/7295561
Sections


text:
Sum of the series 1^1 + 2^2 + 3^3 + ... + n^n using recursion in C++

C++Server Side ProgrammingProgramming

C in Depth: The Complete C Programming Guide for Beginners

45 Lectures 4.5 hours

Practical C++: Learn C++ Basics Step by Step

Most Popular

50 Lectures 4.5 hours

Master C and Embedded C Programming- Learn as you go

66 Lectures 5.5 hours

In this problem, we are given a number n which defines the nth terms of the series 1^1 + 2^2 + 3^3 + … + n^n. Our task is to create a program that will find the sum of the series.

Let’s take an example to understand the problem,

Input

n = 4

Output

30

Explanation −sum = (1^1) + (2^2) + (3^3) + (4^4) = 1 + 4 + 9 + 16 = 30.

To solve this problem, we will loop from 1 to n. Find the square of each number. And add each to the sum variable.

Algorithm

Initialize sum = 0
Step 1: Iterate from i = 1 to n. And follow :
Step 1.1: Update sum, sum += i*i
Step 2: Print sum.

Example

Program to illustrate the working of our solution,

Live Demo

#include <iostream>
using namespace std;
long long calcSeriesSum(int n) {
long long sum = 0;
for( int i = 1; i <= n; i++ )
sum += (i*i);
return sum;
}
int main() {
int n = 7;
cout<<"Sum of the series 1^1 + 2^2 + 3^3 + ... + "<<n<<"^"<<n<<" is "<<calcSeriesSum(n);
return 0;
}

Output

Sum of the series 1^1 + 2^2 + 3^3 + ... + 7^7 is 140
Updated on 14-Aug-2020 14:09:35


text:
# Which distribution has its maximum uniformly distributed?

Let's consider $$Y_n$$ the max of $$n$$ iid samples $$X_i$$ of the same distribution:

$$Y_n = max(X_1, X_2, ..., X_n)$$

Do we know some common distributions for $$X$$ such that $$Y$$ is uniformly distributed $$U(a,b)$$?

I guess we can always "construct a distribution" $$X$$ to enforce this condition for $$Y$$ but I was just wondering if a famous distribution satisfies this condition.

• It is worth noting that the law of any such $X$ must be unique, so "constructing a distribution" will give you the (only) answer.
– πr8
Sep 3 '20 at 7:10
• @πr8 can you elaborate why such a law has to be unique? Sep 3 '20 at 15:34
• math.stackexchange.com/questions/1397427/… Sep 3 '20 at 18:11
• if a maximum $Y$ is a scalar, how can it have a distribution? Sep 4 '20 at 1:00
• @develarist it's not a scalar. It's a sequence defined by $n$ and $X$. Sep 4 '20 at 11:50

Let $$F$$ be the CDF of $$X_i$$. We know that the CDF of $$Y$$ is $$G(y) = P(Y\leq y)= P(\textrm{all } X_i\leq y)= \prod_i P(X_i\leq y) = F(y)^n$$

Now, it's no loss of generality to take $$a=0$$, $$b=1$$, since we can just shift and scale the distribution of $$X$$ to $$[0,\,1]$$ and then unshift and unscale the distribution of $$Y$$.

So what does $$F$$ have to be to get $$G(y) =y$$? We need $$F(x)= x^{1/n}I_{[0,1]}$$, so $$f(x)=\frac{1}{n}x^{1/n-1}I_{[0,1]}$$, which is a Beta(1/n,1) density.

Let's check

> r<-replicate(100000, max(rbeta(4,1/4,1)))
> hist(r)

$$F_{X_{(n)}}(x)=[F_X(x)]^n$$, so for a standard uniform you need $$F_X(x)=x^{1/n}$$ for $$0 (and $$0$$ to the left and $$1$$ to the right of that interval), so $$f_X(x)=\frac{1}{n}x^{\frac{1}{n}-1}$$ on the unit interval and $$0$$ elsewhere.

It's a special case of the beta.


text:
Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Annales Polonici Mathematici

2001 | 77 | 1 | 21-38

## On distance between zeros of solutions of third order differential equations

EN

### Abstrakty

EN
The lower bounds of the spacings b-a or a'-a of two consecutive zeros or three consecutive zeros of solutions of third order differential equations of the form
y''' + q(t)y' + p(t)y = 0 (*)
are derived under very general assumptions on p and q. These results are then used to show that $t_{n+1} - tₙ → ∞$ or $t_{n+2} - tₙ → ∞$ as n → ∞ under suitable assumptions on p and q, where ⟨tₙ⟩ is a sequence of zeros of an oscillatory solution of (*). The Opial-type inequalities are used to derive lower bounds of the spacings d-a or b-d for a solution y(t) of (*) with y(a) = 0 = y'(a), y'(c) = 0 and y''(d) = 0 where d ∈ (a,c) or y'(c) = 0, y(b) = 0 = y'(b) and y''(d) = 0 where d ∈ (c,b).

21-38

wydano
2001

### Twórcy

autor
• Department of Mathematics, Berhampur University, Berhampur 760007, India
autor
• Department of Mathematics, Berhampur University, Berhampur 760007, India


text:
+1 vote
56 views

The sum $\dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n-1)^2} + \cdots \cdots$ is

1. $\frac{\pi}{4}$
2. $\frac{\pi}{8}$
3. $\frac{\pi}{6}$
4. $2 \pi$

recategorized | 56 views
0
$\frac{\pi}{4}?$
0

Is the question same as $\displaystyle \lim_{n\to \infty} \sum_{k=0}^{n}\frac{n}{n^2+k^2}$ ?
$$\mathrm{Or}$$
$\frac{n}{n^2}+\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\cdots+\frac{n}{n^2+(n-1)^2}+\frac{n}{n^2+n^2}+\frac{n}{n^2+(n+1)^2}+\frac{n}{n^2+(n+2)^2}+\cdots$

Which one is it?

0
Both are the same.
0

Nope. Both aren't the same.

$\displaystyle \lim_{n\to \infty} \sum_{k=0}^{n}\frac{n}{n^2+k^2}$ has the last term as $\frac{n}{n^2+n^2}$ where $n\to \infty$.

But $\frac{n}{n^2}+\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\cdots+\frac{n}{n^2+(n-1)^2}+\frac{n}{n^2+n^2}+\frac{n}{n^2+(n+1)^2}+\frac{n}{n^2+(n+2)^2}+\cdots$ can have term $\frac{n}{n^2+(n+n)^2}=\frac{n}{n^2+4n^2}$ and so on.

+1
$\displaystyle \sum_{k=0}^{\infty}\frac{n}{n^2+k^2}$ ?
$$\mathrm{Or}$$
$\displaystyle \frac{n}{n^2}+\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\cdots+\frac{n}{n^2+(n-1)^2}+\frac{n}{n^2+n^2}+\frac{n}{n^2+(n+1)^2}+\frac{n}{n^2+(n+2)^2}+\cdots$

These are same.
0
If so, the answer would be $\frac{\pi}{2}$ which is NOT there in the stated options.

BTW $\displaystyle \lim_{n\to \infty} \sum_{k=0}^{n}\frac{n}{n^2+k^2}=\frac{\pi}{4}$

but $\displaystyle \sum_{k=0}^{\infty}\frac{n}{n^2+k^2}=\frac{\pi}{2}$

So definitely the question has to be
$\displaystyle \lim_{n \to \infty} \left( \dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n-1)^2} +\dfrac{n}{n^2+n^2} \right)$

+1 vote