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 dissipated is $P = V_{rms} I_{rms} \cos\phi$.
$P = \varepsilon \left(\frac{\varepsilon}{Z}\right) \left(\frac{R}{Z}\right) = \frac{\varepsilon^2 R}{Z^2}$.
In a series LCR circuit, $Z^2 = R^2 + (L\omega - \frac{1}{C\omega})^2$.
Thus, $P = \frac{\varepsilon^2 R}{[ R^2 + (L\omega - \frac{1}{C\omega})^2 ]}$.