Question #43471

This question tests the student's ability to analyze AC power in parallel circuits and avoid the trap of ignoring the phase difference (power factor) between the source current and voltage.

Students often incorrectly apply the DC power formula $P = V_{rms} I_{rms}$ without the $\cos\phi$ term, leading to $4\sqrt{5} \text{ mW}$.

Alternatively, they may ignore the internal shunt capacitance entirely, assuming all source current passes through the resistor, yielding $20 \text{ mW}$.

Another common error is forgetting the RMS conversion factor and using peak values $P = V_0 I_0 \cos\phi$, resulting in $8 \text{ mW}$.

The correct approach requires recognizing that the current splits, and average power is only dissipated by the resistive component, which can be found via $P = V_{rms}^2 / R$ or $P = V_{rms} I_{rms} \cos\phi$.