Rankers Physics

Alternating Current: Practice Problem & Solution

39. For a series LCR circuit the power loss at resonance is: (2002)
$\frac{V^2}{[\omega L - \frac{1}{\omega C}]}$
$I^2 L \omega$
$I^2 R$
$\frac{V^2}{C \omega}$

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:

At resonance in a series LCR circuit, $X_L = X_C$, meaning the circuit is purely resistive.
Total impedance $Z = R$.
Power loss is $P = I_{rms}^2 Z \cos\phi$.
Since $\cos\phi = 1$ and $Z = R$, $P = I^2 R$.

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