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
, where
is the voltage at time
,
is the peak voltage, and
is the frequency in hertz.
In a simple circuit,
and AC current is
, where
is the current at time
, and
is the peak current.
The average AC power is
.
Average (rms) current
and average (rms) voltage
are
and
, where rms stands for root mean square.
Thus,
.
Ohm’s law for AC is
.
Expressions for the average power of an AC circuit are
,
, and
, 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.
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.
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?
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
transmission line. (c) What percent loss does this represent?
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
?
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?
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
, is needed if the operating temperature is
? (c) What power will it draw when first switched on?
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