Question:
A series LCR circuit is designed to resonate at an angular frequency \( \omega_0 = 10^5 \) rad/s. The circuit draws 16 W power from a 120 V source at resonance. The value of resistance \( R \) in the circuit is _____ Ω.
A series LCR circuit is designed to resonate at an angular frequency \( \omega_0 = 10^5 \) rad/s. The circuit draws 16 W power from a 120 V source at resonance. The value of resistance \( R \) in the circuit is _____ Ω.
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At resonance, the inductive and capacitive reactances cancel out $(X_L = X_C)$, making the circuit purely resistive.
Updated On: Feb 2, 2026
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Correct Answer: 900
Solution and Explanation
Step 1: At resonance, impedance $Z = R$.
Step 2: Power $P = \frac{V_{rms}^2}{R}$.
Step 3: $16 = \frac{120^2}{R} = \frac{14400}{R}$.
Step 4: $R = \frac{14400}{16} = 900 \ \Omega$.
Step 2: Power $P = \frac{V_{rms}^2}{R}$.
Step 3: $16 = \frac{120^2}{R} = \frac{14400}{R}$.
Step 4: $R = \frac{14400}{16} = 900 \ \Omega$.
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