Alternating Current: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Alternating Current. Understanding the underlying formula is key to arriving at the correct answer below:

$V_{rms} = \frac{V_0}{\sqrt{2}} = \frac{1/\sqrt{2}}{\sqrt{2}} = \frac{1}{2} V$ and $I_{rms} = \frac{I_0}{\sqrt{2}} = \frac{1/\sqrt{2}}{\sqrt{2}} = \frac{1}{2} A$.
The phase difference between voltage and current is $\phi = \frac{\pi}{3}$.
Average power $P = V_{rms} I_{rms} \cos\phi = \frac{1}{2} \times \frac{1}{2} \times \cos(\frac{\pi}{3})$.
$P = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} W$.