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:

Average power is given by $P_{avg} = E_{rms} I_{rms} \cos\phi$.
Substituting RMS values: $E_{rms} = \frac{E_0}{\sqrt{2}}$ and $I_{rms} = \frac{I_0}{\sqrt{2}}$.
$P_{avg} = \left(\frac{E_0}{\sqrt{2}}\right) \left(\frac{I_0}{\sqrt{2}}\right) \cos\phi$.
$P_{avg} = \frac{E_0 I_0}{2} \cos\phi$.