20.1

Electromotive Force and Current

Look around you. Chances are that there is an electrical device nearby—a radio, a hair dryer, a computer—something that uses electrical energy to operate. The energy needed to run a portable CD player, for instance, comes from batteries, as Figure 20-1 illustrates. The transfer of energy takes place via an electric circuit, in which the energy source (the battery pack) and the energy-consuming device (the CD player) are connected by conducting wires, through which electric charges move.

Figure 20-1 In an electric circuit, energy is transferred from a source (the battery pack) to a device (the CD player) by charges that move through a conducting wire.

Within a battery, a chemical reaction occurs that transfers electrons from one terminal (leaving it positively charged) to another terminal (leaving it negatively charged). Figure 20-2 shows the two terminals of a car battery and a flashlight battery. The drawing also illustrates the symbol used to represent a battery in circuit drawings. Because of the positive and negative charges on the battery terminals, an electric potential difference exists between them. The maximum potential difference is called the electromotive force* (emf) of the battery, for which the symbol E is used. In a typical car battery, the chemical reaction maintains the potential of the positive terminal at a maximum of 12 volts (12 joules/coulomb) higher than the potential of the negative terminal, so the emf is . Thus, one coulomb of charge emerging from the battery and entering a circuit has at most 12 joules of energy. In a typical flashlight battery the emf is 1.5 V. In reality, the potential difference between the terminals of a battery is somewhat less than the maximum value indicated by the emf, for reasons that Section 20.9 discusses.

Figure 20-2 Typical batteries and the symbol used to represent them in electric circuits.

In a circuit such as that in Figure 20-1, the battery creates an electric field within and parallel to the wire, directed from the positive toward the negative terminal. The electric field exerts a force on the free electrons in the wire, and they respond by moving. Figure 20-3 shows charges moving inside a wire and crossing an imaginary surface that is perpendicular to their motion. This flow of charge is known as an electric current. The electric current I is defined as the amount of charge per unit time that crosses the imaginary surface, as in Figure 20-3, in much the same sense that a river current is the amount of water per unit of time that is flowing past a certain point. If the rate is constant, the current is

| (20.1)

If the rate of flow is not constant, then Equation 20.1 gives the average current. Since the units for charge and time are the coulomb (C) and the second (s), the SI unit for current is a coulomb per second (C/s). One coulomb per second is referred to as an ampere (A), after the French mathematician André-Marie Ampère (1775–1836).

Figure 20-3 The electric current is the amount of charge per unit time that passes through an imaginary surface that is perpendicular to the motion of the charges.

If the charges move around a circuit in the same direction at all times, the current is said to be direct current (dc), which is the kind produced by batteries. In contrast, the current is said to be alternating current (ac) when the charges move first one way and then the opposite way, changing direction from moment to moment. Many energy sources produce alternating current—for example, generators at power companies and microphones. Example 1 deals with direct current.

| Example 1 | | | A Pocket Calculator

The battery pack of a pocket calculator has a voltage* of 3.0 V and delivers a current of 0.17 mA. In one hour of operation, (a) how much charge flows in the circuit and (b) how much energy does the battery deliver to the calculator circuit?
Reasoning Since current is defined as charge per unit time, the charge that flows in one hour is the product of the current and the time (3600 s). The charge that leaves the 3.0-V battery pack has 3.0 joules of energy per coulomb of charge. Thus, the total energy delivered to the calculator circuit is the charge (in coulombs) times the energy per unit charge (in volts or joules/coulomb).
Solution

a. | The charge that flows in one hour can be determined from Equation 20.1:

b. | The energy delivered to the calculator circuit is

Today, it is known that electrons flow in metal wires. Figure 20-4 shows the negative electrons emerging from the negative terminal of the battery and moving around the circuit toward the positive terminal. It is customary, however, not to use the flow of electrons when discussing circuits. Instead, a so-called conventional current is used, for reasons that date to the time when it was believed that positive charges moved through metal wires. Conventional current is the hypothetical flow of positive charges that would have the same effect in the circuit as the movement of negative charges that actually does occur. In Figure 20-4, negative electrons leave the negative terminal of the battery, pass through the device, and arrive at the positive terminal. The same effect would have been achieved if an equivalent amount of positive charge had left the positive terminal, passed through the device, and arrived at the negative terminal. Therefore, the drawing shows the conventional current originating from the positive terminal. A conventional current of hypothetical positive charges is consistent with our earlier use of a positive test charge for defining electric fields and potentials. The direction of conventional current is always from a point of higher potential toward a point of lower potential—that is, from the positive toward the negative terminal. In this text, the symbol I stands for conventional current.

Figure 20-4 In a circuit, electrons actually flow through the metal wires. However, it is customary to use a conventional current I to describe the flow of charges.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.