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A series LCR circuit is designed to resonate at an angular frequency $$\omega_0 = 10^5$$ rad s$$^{-1}$$. The circuit draws 16 W power from 120 V source at resonance. The value of resistance $$R$$ in the circuit is ______ $$\Omega$$.
Correct Answer: 900
In a series LCR circuit at resonance, the impedance of the circuit equals the resistance $$R$$ alone, because the inductive and capacitive reactances cancel each other out ($$X_L = X_C$$). Therefore, the circuit behaves as a purely resistive circuit at resonance.
The power drawn from the source at resonance is given by $$P = \frac{V^2}{R}$$, where $$V = 120$$ V is the source voltage and $$P = 16$$ W is the power consumed.
Solving for $$R$$: $$R = \frac{V^2}{P} = \frac{(120)^2}{16} = \frac{14400}{16} = 900 \; \Omega$$.
Therefore, the value of resistance $$R$$ in the circuit is $$900 \; \Omega$$.
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