Introductory Physics Volume Two

6.7 AC Circuit Elements 123
+
V S–
R
Because the current oscillates in time, the power dissipated in the resistor
also oscillates in time.
P (t) = I(t)V (t)
= I(t)I(t)R
= [I(t)] 2 R
= [I 0 cos ωt] 2 R
= I 2 0 R cos 2 ωt
Notice that the power oscillates between zero and I 2 0 R so that the
average power supplied to the toaster is 1 2 I2 0 R.
P avg = I2 0 R
= I 0 I
√ 0 R √2 = I 0 V
√ √ 0
= (7.0A)(120V)
2 2 2 2
Notice that for a sinusoidal signal the root mean square (RMS) value is
the amplitude divided by √ 2. Thus we can learn two things from this
example. First, the values that are printed on the toaster are the RMS
values. Second, the product of the RMS current and RMS voltage gives
the average power. So in this example the average power consumed by
the appliance is P = (7.0A)(120V) = 840W.
⊲ Problem 6.4
A 60 watt light bulb has an average power output of 60 watts.
(a) What is the peak power?
(b) What is the resistance of the bulb?
(c) Is this resistance the same as the resistance that is required to
dissipate 60 watts when connected to a 120 volt DC source?
§ 6.7 AC Circuit Elements
In many ways an AC circuit can be analyzed using the same techniques
we used for DC circuits. In fact inductors and capacitors become
as simple as resistors. In an AC circuit, inductors and capacitors
follow an adapted Ohm’s Law: the amplitude of the voltage on the