Chapter 26, Problem 1CQ

Identical resistors are connected to separate 12 V AC sources. One source operates at 60 Hz, the other at 120 Hz. In which circuit, if either, does the resistor dissipate the greater average power?

To determine

Which circuit dissipates more average power.

Answer to Problem 1CQ

The power dissipated in both circuits is same.

Explanation of Solution

The expression to find the average power dissipated by a resistor in an AC circuit is given as follows.

$P_{\text{R}}=\frac{{\left(V_{\text{rms}}\right)}^2}{R}$ (1)

Here,

$P_{\text{R}}$ is the power dissipated in a resistance,

$V_{\text{rms}}$ is the rms voltage, and

R is the resistance circular path of radius.

The rms voltage value of 60 Hz AC source and 120 Hz AC source is 12 V.

From (1), it can be defined that the average power dissipation is directly proportional to square of the rms voltage and does not depend on the operating frequency. So, the average power dissipation remains constant irrespective of frequency changes with same rms voltage.

Therefore, the average power dissipated by a resistor in both circuits (a circuit with 60 Hz AC source and a circuit with 120 Hz Ac source) is same.

Conclusion:

Hence, the power dissipated in both circuits is same.