# 3.5 Alternating current versus direct current  (Page 4/10)

 Page 4 / 10

## Phet explorations: generator

Generate electricity with a bar magnet! Discover the physics behind the phenomena by exploring magnets and how you can use them to make a bulb light.

## Section summary

• Direct current (DC) is the flow of electric current in only one direction. It refers to systems where the source voltage is constant.
• The voltage source of an alternating current (AC) system puts out $V={V}_{0}\phantom{\rule{0.25em}{0ex}}\text{sin 2}\pi \text{ft}$ , where $V$ is the voltage at time $t$ , ${V}_{0}$ is the peak voltage, and $f$ is the frequency in hertz.
• In a simple circuit, $I=\text{V/R}$ and AC current is $I={I}_{0}\phantom{\rule{0.25em}{0ex}}\text{sin 2}\pi \text{ft}$ , where $I$ is the current at time $t$ , and ${I}_{0}={V}_{0}\text{/R}$ is the peak current.
• The average AC power is ${P}_{\text{ave}}=\frac{1}{2}{I}_{0}{V}_{0}$ .
• Average (rms) current ${I}_{\text{rms}}$ and average (rms) voltage ${V}_{\text{rms}}$ are ${I}_{\text{rms}}=\frac{{I}_{0}}{\sqrt{2}}$ and ${V}_{\text{rms}}=\frac{{V}_{0}}{\sqrt{2}}$ , where rms stands for root mean square.
• Thus, ${P}_{\text{ave}}={I}_{\text{rms}}{V}_{\text{rms}}$ .
• Ohm’s law for AC is ${I}_{\text{rms}}=\frac{{V}_{\text{rms}}}{R}$ .
• Expressions for the average power of an AC circuit are ${P}_{\text{ave}}={I}_{\text{rms}}{V}_{\text{rms}}$ , ${P}_{\text{ave}}=\frac{{V}_{\text{rms}}^{\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}2}}{R}$ , and ${P}_{\text{ave}}={I}_{\text{rms}}^{\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}2}R$ , analogous to the expressions for DC circuits.

## Conceptual questions

Give an example of a use of AC power other than in the household. Similarly, give an example of a use of DC power other than that supplied by batteries.

Why do voltage, current, and power go through zero 120 times per second for 60-Hz AC electricity?

You are riding in a train, gazing into the distance through its window. As close objects streak by, you notice that the nearby fluorescent lights make dashed streaks. Explain.

## Problem exercises

(a) What is the hot resistance of a 25-W light bulb that runs on 120-V AC? (b) If the bulb’s operating temperature is $\text{2700º}\text{C}$ , what is its resistance at $\text{2600º}\text{C}$ ?

Certain heavy industrial equipment uses AC power that has a peak voltage of 679 V. What is the rms voltage?

480 V

A certain circuit breaker trips when the rms current is 15.0 A. What is the corresponding peak current?

Military aircraft use 400-Hz AC power, because it is possible to design lighter-weight equipment at this higher frequency. What is the time for one complete cycle of this power?

2.50 ms

A North American tourist takes his 25.0-W, 120-V AC razor to Europe, finds a special adapter, and plugs it into 240 V AC. Assuming constant resistance, what power does the razor consume as it is ruined?

In this problem, you will verify statements made at the end of the power losses for [link] . (a) What current is needed to transmit 100 MW of power at a voltage of 25.0 kV? (b) Find the power loss in a $1\text{.}\text{00 -}\phantom{\rule{0.25em}{0ex}}\Omega$ transmission line. (c) What percent loss does this represent?

(a) 4.00 kA

(b) 16.0 MW

(c) 16.0%

A small office-building air conditioner operates on 408-V AC and consumes 50.0 kW. (a) What is its effective resistance? (b) What is the cost of running the air conditioner during a hot summer month when it is on 8.00 h per day for 30 days and electricity costs $9.00 cents\text{/kW}\cdot \text{h}$ ?

What is the peak power consumption of a 120-V AC microwave oven that draws 10.0 A?

2.40 kW

What is the peak current through a 500-W room heater that operates on 120-V AC power?

Two different electrical devices have the same power consumption, but one is meant to be operated on 120-V AC and the other on 240-V AC. (a) What is the ratio of their resistances? (b) What is the ratio of their currents? (c) Assuming its resistance is unaffected, by what factor will the power increase if a 120-V AC device is connected to 240-V AC?

(a) 4.0

(b) 0.50

(c) 4.0

Nichrome wire is used in some radiative heaters. (a) Find the resistance needed if the average power output is to be 1.00 kW utilizing 120-V AC. (b) What length of Nichrome wire, having a cross-sectional area of $5.00{\text{mm}}^{2}$ , is needed if the operating temperature is $\text{500º C}$ ? (c) What power will it draw when first switched on?

Find the time after $t=0$ when the instantaneous voltage of 60-Hz AC first reaches the following values: (a) ${V}_{0}/2$ (b) ${V}_{0}$ (c) 0.

(a) 1.39 ms

(b) 4.17 ms

(c) 8.33 ms

(a) At what two times in the first period following $t=0$ does the instantaneous voltage in 60-Hz AC equal ${V}_{\text{rms}}$ ? (b) $-{V}_{\text{rms}}$ ?

#### Questions & Answers

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Salomon
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Salomon
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