A series LCR circuit is designed to resonate | vedclass

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(D) At resonance,the inductive reactance $X_{L}$ and capacitive reactance $X_{C}$ cancel each other out,meaning the total impedance of the circuit is

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$900$

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(D) At resonance,the inductive reactance $X_{L}$ and capacitive reactance $X_{C}$ cancel each other out,meaning the total impedance of the circuit is equal to the resistance $R$,i.e.,$Z = R$.The power consumed in an $LCR$ circuit at resonance is given by the formula:$P = \frac{V^{2}}{R}$Given values are:$P = 16 \, W$$V = 120 \, V$Rearranging the formula to solve for $R$:$R = \frac{V^{2}}{P}$Substituting the values:$R = \frac{(120)^{2}}{16}$$R = \frac{14400}{16}$$R = 900 \, \Omega$Thus,the value of resistance $R$ is $900 \, \Omega$.

$A$ 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 ...... $\Omega$.

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