20.4

Electric Power

One of the most important functions of the current in an electric circuit is to transfer energy from a source (such as a battery or a generator) to an electrical device (CD player, cell phone, etc.), as Figure 20-9 illustrates. Note that the positive (+) terminal of the battery is connected by a wire to the terminal labeled A on the device; likewise, the negative terminal (−) of the battery is connected to the B terminal. Thus, the battery maintains a constant potential difference between the terminals A and B, with A being at the higher potential. When an amount of positive charge moves from the higher potential (A) to the lower potential (B), its electric potential energy decreases. In accordance with Equation 19.4, this decrease is , where V is the amount by which the electric potential at A exceeds that at B, or, in other words, the voltage between the two points. Since the change in energy per unit time is the power P (Equation 6.10b), the electric power associated with this change in energy is

The term is the charge per unit time, or the current I in the device, according to Equation 20.1. Thus, the electric power is the product of the current and the voltage.

Electric utility companies are planning for the replacement of power lines with high-temperature superconducting cables. These workmen are feeding a test cable through an existing passage at a power station. (Andrew Sacks/saxpix.com)

| Electric Power
| When electric charge flows from point A to point B in a circuit, leading to a current I, and the voltage between the points is V, the electric power associated with this current and voltage is

| (20.6)

SI Unit of Power: watt (W)

Power is measured in watts, and Equation 20.6 indicates that the product of an ampere and a volt is equal to a watt.
When the charge moves through the device in Figure 20-9, the charge loses electric potential energy. The principle of conservation of energy tells us that the decrease in potential energy must be accompanied by a transfer of energy to some other form (or forms). In a cell phone, for example, the energy transferred appears as light energy (coming from the display screen), sound energy (emanating from the speaker), thermal energy (due to heating of the internal circuitry), and so on.

Figure 20-9 The current I in the circuit delivers energy to the electric device. The voltage between the terminals of the device is V.

The charge in a circuit can also gain electrical energy. For example, when it moves through the battery in Figure 20-9, the charge goes from a lower to a higher potential, just the opposite of what happens in the electrical device. In this case, the charge gains electric potential energy. Consistent with the conservation of energy, this increase in potential energy must come from somewhere; in this case it comes from the chemical energy stored in the battery. Thus, the charge regains the energy it lost to the device, at the expense of the chemical energy of the battery.
Many electrical devices are essentially resistors that become hot when provided with sufficient electric power: toasters, irons, space heaters, heating elements on electric stoves, and incandescent light bulbs, to name a few. In such cases, it is possible to obtain two additional, but equivalent, expressions for the power. These two expressions follow directly upon substituting V = IR, or equivalently I = V/R, into the relation P = IV:

| (20.6a)

| (20.6b)

| (20.6c)

Example 5 deals with the electric power delivered to the bulb of a flashlight.

| Example 5 | | | The Power and Energy Used in a Flashlight

In the flashlight in Figure 20-6, the current is 0.40 A, and the voltage is 3.0 V. Find (a) the power delivered to the bulb and (b) the electrical energy dissipated in the bulb in 5.5 minutes of operation. Reasoning The electric power delivered to the bulb is the product of the current and voltage. Since power is energy per unit time, the energy delivered to the bulb is the product of the power and time.
Solution

a. | The power is

| (20.6a)

The “wattage” rating of this bulb would, therefore, be 1.2 W.
b. | The energy consumed in 5.5 minutes (330 s) follows from the definition of power as energy per unit time:

Monthly electric bills specify the cost for the energy consumed during the month. Energy is the product of power and time, and electric companies compute your energy consumption by expressing power in kilowatts and time in hours. Therefore, a commonly used unit for energy is the kilowatt · hour (kWh). For instance, if you used an average power of 1440 watts (1.44 kW) for 30 days (720 h), your energy consumption would be (1.44 kW)(720 h) = 1040 kWh. At a cost of $0.12 per kWh, your monthly bill would be $125. As shown in Example 10 in Chapter 12, of energy.

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