Chapter 23, Problem 1FC

To determine

The correct option for change in average power dissipated in the resistor when the frequency is doubled and the rms voltage is tripled.

Answer to Problem 1FC

The correct option is (d). The average power increases by a factor 3² = 9 because it proportional to the square of the rms voltage.

Explanation of Solution

Given data:

A circuit contains an ac generator and a resistor.

Frequency is doubled and the rms voltage tripled.

Formula used:

Write the expression for average power delivered.

$\overline{P}=\frac{V_{\text{rms}}^2}{R}$ (1)

Here,

$V_{\text{rms}}$ is the root mean square (rms) voltage across the resistor, and

$R$ is the resistance.

Explanation:

In general, the value of resistance is independent of frequency of AC generator. Therefore, average power of the circuit with resistance is independent of frequency.

Substitute $3V_{\text{rms}}$ for $V_{\text{rms}}$ in equation (1),

$\begin{array}{c}\overline{P}=\frac{{\left(3V_{\text{rms}}\right)}^2}{R}\\ =\frac{9V_{\text{rms}}^2}{R}\end{array}$

Therefore, by doubling the frequency and tripling the rms voltage, the average power increases by a factor $9$ that is option (d) is correct and remaining options (a), (b), (c) and (e) are in correct.

Conclusion:

Hence, the correct option is (d). The average power increases by a factor 3² = 9 because it proportional to the square of the rms voltage.