Emf and Internal Resistance

9 Key excerpts on "Emf and Internal Resistance"

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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  The electro- motive force (emf) of a generator, such as a battery, is the maximum potential difference (in volts) that exists between the terminals of the generator. The rate of flow of charge is called the electric current. If the rate is con- stant, the current I is given by Equation 20.1, where ∆q is the magnitude of the charge crossing a surface in a time Δt, the surface being perpendicular to the motion of the charge. The SI unit for current is the coulomb per second (C/s), which is referred to as an ampere (A). When the charges flow only in one direction around a circuit, the current is called direct current (dc). When the direction of charge flow changes from moment to moment, the current is known as alternating current (ac). Conventional current is the hypothetical flow of positive charges that would have the same effect in a circuit as the movement of negative charges that actually does occur. I = ∆q ∆t (20.1) 20.2 Ohm’s Law The definition of electrical resistance R is R = V/I, where V (in volts) is the voltage applied across a piece of material and I (in amperes) is the current through the material. Resistance is measured in volts per ampere, a unit called an ohm (Ω). If the ratio of the voltage to the current is constant for all values of voltage and current, the resistance is constant. In this event, the definition of resistance becomes Ohm’s law, Equation 20.2. V I = R = constant or V = IR (20.2) 20.3 Resistance and Resistivity The resistance of a piece of material of length L and cross-sectional area A is given by Equation 20.3, where  is the resistivity of the material. The resistivity of a material depends on the tem- perature. For many materials and limited temperature ranges, the temperature dependence is given by Equation 20.4, where  and  0 are the resistivities at the temperatures T and T 0 , respectively, and  is the temperature coefficient of resistivity.

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  Introduction to Electrodynamics

  • David J. Griffiths(Author)
  • 2017(Publication Date)
  • Cambridge University Press

    (Publisher)

  However, as you’ll see in the next section, there is some subtlety in- volved in this interpretation, so I prefer Eq. 7.9. 4 Real batteries have a certain internal resistance, r , and the potential difference between their termi- nals is E − Ir , when a current I is flowing. For an illuminating discussion of how batteries work, see D. Roberts, Am. J. Phys. 51, 829 (1983). 5 Current in an electric circuit is somewhat analogous to the flow of water in a closed system of pipes, with gravity playing the role of the electrostatic field, and a pump (lifting the water up against gravity) in the role of the battery. In this story height is analogous to voltage. 7.1 Electromotive Force 305 Problem 7.5 A battery of emf E and internal resistance r is hooked up to a variable “load” resistance, R. If you want to deliver the maximum possible power to the load, what resistance R should you choose? (You can’t change E and r , of course.) −σ +σ E R h FIGURE 7.9 Problem 7.6 A rectangular loop of wire is situated so that one end (height h) is between the plates of a parallel-plate capacitor (Fig. 7.9), oriented parallel to the field E. The other end is way outside, where the field is essentially zero. What is the emf in this loop? If the total resistance is R, what current flows? Explain. [Warning: This is a trick question, so be careful; if you have invented a perpetual motion machine, there’s probably something wrong with it.] 7.1.3 Motional emf In the last section, I listed several possible sources of electromotive force, batteries being the most familiar. But I did not mention the commonest one of all: the generator. Generators exploit motional emfs, which arise when you move a wire through a magnetic field. Figure 7.10 suggests a primitive model for a generator. In the shaded region there is a uniform magnetic field B, pointing into the page, and the resistor R represents whatever it is (maybe a light bulb or a toaster) we’re trying to drive current through.

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  Reeds Vol 16: Electrical Power Systems for Marine Engineers

  • Gordon Boyd, Fred Taylor(Authors)
  • 2020(Publication Date)
  • Reeds

    (Publisher)

  More simply, e.m.f. can be expressed as the potential difference existing between the terminals when the generator or cell is at open circuit, i.e. when no current is flowing. Every e.m.f. is a potential difference, but not every potential difference is an e.m.f.

  For example, there is a potential difference existing across the pins of a lamp holder when the circuit switch is in the ON position regardless of whether the lamp is inserted or not, but it is not an e.m.f.

  Potential difference, expressed by the letter V , exists when current flows.

  In simplistic terms it can be considered that a generator or cell is capable of producing an e.m.f. before load is applied. When connected to a load and with current flowing, a difference of potential exists. Generally this means that there is a discrepancy between e.m.f. and p.d. in terms of actual values.

  Resistance in series and in parallel

  For a given voltage the amount of electric current that will flow in a circuit is determined by the ease with which each part of the circuit allows the current to pass. Every circuit offers some opposition to current flow. This opposition is called resistance , and is measured in ohms (circuit symbol Ω). A component having a definite value of resistance is called a resistor .

  1. Grouping of resistances

  In practice, an electrical circuit consists of a number of parts, wires, items of equipment, etc. connected together in various ways. Consider three loads having resistance of R 1, R 2, R 3 respectively.

  They could be connected in series (Figure 2.5 ):

  Figure 2.5 Resistors in series

  or in parallel (Figure 2.6 ):

  Figure 2.6 Resistors in parallel

  or in a combination of both (Figure 2.7 ):

  Figure 2.7 Resistors in series and parallel

  2. Series connection

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  N3 Engineering Science

  • T Ferreira(Author)
  • 2013(Publication Date)
  • Future Managers

    (Publisher)

  7 CHAPTER Electricity 7.1 Cells 7.1.1 Internal resistance The simplest contributing factor to the internal resistance of a cell is the resistance of the materials from which the cell is constructed. Examples of more complicated contributing factors are temperature, polarisation and crystalisation of the plates. Some of these are once again dependent on the type of cell being considered, e.g. primary or secondary cells, lead acid cells or nicad cells. A deeper discussion is beyond the scope of the syllabus but the effects of the internal resistance are of importance. Experiment 7.1 Internal resistance Requirements: A motor car and a voltmeter. • Disconnect the high voltage lead from the coil to the distributor at the distributor, and allow it to touch a part of the bodywork (safety). This is done to prevent the car from starting. • Connect the voltmeter across the battery. The reading of this open-circuit or no-load voltage is known as the emf (electromotive force [E]) of the battery. The value should be about 13 V. (Refer to fig. 7.1(a).) • Switch the headlights on and notice how the terminal voltage decreases to about 12,5 V. This is referred to as the on-load voltage and denoted by V. (Refer to fig. 7.1(b).) • Turn the ignition switch, and notice how the large current drawn by the starter motor causes an even lower voltage (V) at the terminals. The reading should be in the region of 10 to 11 V. Result An internal volt drop occurs as a result of an internal resistance. This causes the terminal voltage to drop and is obviously dependent on the load current. Refer to fig. 7.1(a). When the switch is open, the emf “E” is equal to the terminal voltage “V”. When the switch is closed, a current “I” flows through the external resistor “R”, as well as through the internal resistance r. This current flow through the internal resistance results, according to Ohm’s law, in an internal volt drop Ir, i.e.

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  OAT Prep Plus 2023-2024

  2 Practice Tests + Proven Strategies + Online

  • (Author)
  • 2023(Publication Date)
  • Kaplan Test Prep

    (Publisher)

  alternating current (AC), in which the flow changes direction periodically. The OAT does not test AC current, so this chapter will only focus on DC current.

  When two points at different electric potentials are connected by a conductor such as a metal wire, charge flows between the two points. In a conductor, only negatively charged electrons are free to move. These act as the charge carriers and move from low to high potentials. By convention, however, the direction of the current is taken as the direction in which positive charge would flow, which is from high to low potential. Thus, the direction of current is opposite the direction of electron flow. Current flows from higher potential (the positive terminal of a battery) to lower potential (the negative terminal of a battery) in the same way that a mass will fall from higher to lower heights in a gravitational field.

  A voltage (potential difference) can be produced by an electric generator, a voltaic cell, or a group of cells wired into a battery. Electromotive force (emf or ε) is the voltage across the terminals of a cell when no current is flowing. Despite its name, electromotive force is not actually a force and should not be confused with forces or electric fields; it is instead a potential difference and is measured in volts.

  When a cell is supplying current it is discharging, and the current flows out of the positive terminal and into the negative terminal. When a cell is being recharged, current from another source is sent into the positive terminal. Ideally, a cell has no internal resistance, and all of the potential is available as ε. However, in the real world, a cell has an internal resistance, Rint , and the available voltage is decreased such that V–IRint = ε. Thus, a real-world cell provides less voltage than an ideal cell.

  Resistance

  Resistance and Ohm’s law

  Resistance (R) can be thought of as the opposition to the flow of an electric current that occurs within a conductor. This opposition takes the form of an energy loss or drop in potential. Ohm’s law states that the voltage drop across a resistor is proportional to the current it carries, with R

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  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  Currents of approximately 0.2 A are potentially fatal because they can make the heart fibrillate, or beat in an uncontrolled manner. Substantially larger currents stop the heart completely. However, since the heart often begins beating normally again after the current ceases, the larger currents can be less dangerous than the smaller currents that cause fibrillation. CONCEPT SUMMARY 20.1 Electromotive Force and Current There must be at least one source or generator of electrical energy in an electric circuit. The electromotive force (emf) of a generator, such as a battery, is the maximum potential difference (in volts) that exists between the terminals of the generator. The rate of flow of charge is called the electric current. If the rate is constant, the current I is given by Equation 20.1, where Dq is the magnitude of the charge crossing a surface in a time Dt, the surface being perpendicular to the motion of the charge. The SI unit for current is the coulomb per second (C/s), which is referred to as an ampere (A). When the charges flow only in one direction around a circuit, the current is called direct current (dc). When the direction of charge flow changes from moment to moment, the current is known as alternating current (ac). Conventional current is the hypothetical flow of positive charges that would have the same effect in a circuit as the movement of negative charges that actually does occur. 20.2 Ohm’s Law The definition of electrical resistance R is R 5 V/I, where V (in volts) is the voltage applied across a piece of material and I (in amperes) is the current through the material. Resistance is measured in volts per ampere, a unit called an ohm (V). If the ratio of the voltage to the current is constant for all values of voltage and current, the resistance is constant. In this event, the definition of resistance becomes Ohm’s law, Equation 20.2.

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  Electrotechnics N4 Student's Book

  TVET FIRST

  • SA Chuturgoon(Author)
  • 2021(Publication Date)
  • Troupant

    (Publisher)

  This internal resistance produces an internal voltage drop as soon as the circuit is closed or when current begins to flow. Formula for calculating the internal voltage drop The internal voltage drop is calculated using the formula: V int = Ir where: • V int = internal voltage drop in volts (V). • I = current in amperes (A). • r = internal resistance in ohms (Ω). Figure 1.19: Internal voltage drop Formula for a circuit using a battery as source of energy The following formula applies to any circuit using a battery as the source of energy: emf = PD + internal voltage drop ( V int ) OR E = V + Ir = IR + Ir [From Ohm’s law: V = IR ] = I ( R + r ) ∴ I = E _______ R + r internal resistance: the resistance of the internal components of a cell or battery internal voltage drop: decrease in electrical potential caused by the current flowing through the internal components of a battery Internal resistance Watch this experiment to learn more about the internal resistance of batteries – Internal resistance experiment by Future Series | https://youtu. be/7b1j7j_P84M See it online 24 Module 1 TVET FIRST where: • I = current in amperes (A). • E = emf in volts (V). • R = external resistance in ohms (Ω). • r = internal resistance in ohms (Ω). Note the difference in the following formulae to calculate total current in a circuit: • I total = E total __________ R total + r total • I total = V total ____ R total Important You have already learned that a battery is made up of two or more identical cells and that these cells can be connected either in series or in parallel. Let us look at how to calculate the total emf ( E total ) and the total internal resistance ( r total ) for cells connected in series and cells connected in parallel. 1.3.2 Cells connected in series Figure 1.20 shows a battery with three identical cells connected in series.

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  Electrical Engineering Fundamentals

  • S. Bobby Rauf(Author)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  The term “electromotive” force stems from the early recognition of electrical current as something that consisted, strictly, of the movement of “electrons.” Nowadays, however, with the more recent breakthroughs in the renewable and non-traditional electrical power generating methods and systems like microbial fuel cells and hydrocarbon fuel cells, electrical power is being harnessed, more and more, in the form of charged particles that may not be electrons. In batteries, such as those used in automobiles, as we will see in the batteries chapter, the flow of current driven by voltage potential difference consists not only of negatively charged electrons, e −, but also types of ions, including H + and HSO 4 − ions. 1 Two, relatively putative, analogies for voltage in the mechanical and civil engineering disciplines are pressure and elevation. In the mechanical realm – or more specifically in the fluid and hydraulic systems – high pressure or pressure differential pushes fluid from one point to another and performs mechanical work. Similarly, voltage – in the form of voltage difference between two points, as with the positive and negative terminals of an automobile battery – moves electrons or charged particles through loads such as motors, coils, resistive elements, wires, or conductors. As electrons or charged particles are pushed through loads like motors, coils, resistive elements, light filaments, etc., electrical energy is converted into mechanical energy, heat energy, or light energy. In equipment like rechargeable batteries, during the charging process, applied voltage can push ions from one electrode (or terminal) to another and thereby “charge” the battery

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  Introduction to Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  The terminal voltage is the voltage between the terminals of a battery or generator and is equal to the emf only when there is no current through the device. When there is a current I, the internal resistance r causes the terminal voltage to be less than the emf by an amount Ir. 20.10 Kirchhoff’s Rules Kirchhoff’s junction rule states that the sum of the magnitudes of the cur- rents directed into a junction equals the sum of the magnitudes of the currents directed out of the junction. Kirchhoff’s loop rule states that, around any closed-circuit loop, the sum of the potential drops equals the sum of the potential rises. The Reasoning Strategy given at the end of Section 20.10 explains how these two rules are applied to analyze any circuit. 20.11 The Measurement of Current and Voltage A galvanometer is a device that responds to electric current and is used in nondigital ammeters and voltmeters. An ammeter is an instrument that measures current and must be inserted into a circuit in such a way that the current passes directly through the ammeter. A voltmeter is an instrument for measuring the voltage between two points in a circuit. A voltmeter must be connected between the two points and is not inserted into a circuit as an ammeter is. 20.12 Capacitors in Series and in Parallel The equivalent capacitance C P for a parallel combination of capacitances (C 1 , C 2 , C 3 , etc.) is given by Equation 20.18. In general, each capacitor in a parallel combination carries a different amount of charge. The equivalent capacitor carries the same total charge and stores the same total energy as the parallel combination. The reciprocal of the equivalent capacitance C S for a series combination (C 1 , C 2 , C 3 , etc.) of capac- itances is given by Equation 20.19. The equivalent capacitor carries the same amount of charge as any one of the capacitors in the combination and stores the same total energy as the series combination.

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