Chapter 15 Electric Current, Resistance, and Ohm’s Law
Chapter 15 Electric Current, Resistance, and Ohm’s Law
15.5 Alternating Current versus Direct Current
Summary
- Explain the differences and similarities between AC and DC current.
- Calculate rms voltage, current, and average power.
- Explain why AC current is used for power transmission.
Alternating Current
Most of the examples dealt with so far, and particularly those utilizing batteries, have constant voltage sources. Once the current is established, it is thus also a constant. Direct current (DC) is the flow of electric charge in only one direction. It is the steady state of a constant-voltage circuit. Most well-known applications, however, use a time-varying voltage source. Alternating current (AC) is the flow of electric charge that periodically reverses direction. If the source varies periodically, particularly sinusoidally, the circuit is known as an alternating current circuit. Examples include the commercial and residential power that serves so many of our needs. Figure 1 shows graphs of voltage and current versus time for typical DC and AC power. The AC voltages and frequencies commonly used in homes and businesses vary around the world.
Figure 2 shows a schematic of a simple circuit with an AC voltage source. The voltage between the terminals fluctuates as shown, with the AC voltage given by
where [latex]\boldsymbol{V}[/latex] is the voltage at time [latex]\boldsymbol{t}[/latex], [latex]\boldsymbol{V_0}[/latex] is the peak voltage, and [latex]\boldsymbol{f}[/latex] is the frequency in hertz. For this simple resistance circuit, [latex]\boldsymbol{I = V/R}[/latex], and so the AC current is
where [latex]\boldsymbol{I}[/latex] is the current at time [latex]\boldsymbol{t}[/latex], and [latex]\boldsymbol{I_0 = V_0/R}[/latex] is the peak current. For this example, the voltage and current are said to be in phase, as seen in Figure 1(b).
Current in the resistor alternates back and forth just like the driving voltage, since [latex]\boldsymbol{I = V/R}[/latex]. If the resistor is a fluorescent light bulb, for example, it brightens and dims 120 times per second as the current repeatedly goes through zero. A 120-Hz flicker is too rapid for your eyes to detect, but if you wave your hand back and forth between your face and a fluorescent light, you will see a stroboscopic effect evidencing AC. The fact that the light output fluctuates means that the power is fluctuating. The power supplied is [latex]\boldsymbol{P = IV}[/latex]. Using the expressions for [latex]\boldsymbol{I}[/latex] and [latex]\boldsymbol{V}[/latex] above, we see that the time dependence of power is [latex]\boldsymbol{P = I_0 V_0 \;\textbf{sin}^2 \; 2 \pi ft}[/latex], as shown in Figure 3.
Making Connections: Take-Home Experiment—AC/DC Lights
Wave your hand back and forth between your face and a fluorescent light bulb. Do you observe the same thing with the headlights on your car? Explain what you observe. Warning: Do not look directly at very bright light.
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