An oscillating circuit consists of a capacito | vedclass

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Question

(A) Given: $R = 10 \, \Omega$, $L = 6.0 \, \mu H = 6.0 	imes 10^{-6} \, H$, $C = 10 \, \mu F = 10 	imes 10^{-6} \, F$, $f = 50 \, Hz$, $V_m = 280 \,

Vedclass · Accepted Answer

$3.8 \, W$

Vedclass · Answer

(A) Given: $R = 10 \, \Omega$, $L = 6.0 \, \mu H = 6.0 	imes 10^{-6} \, H$, $C = 10 \, \mu F = 10 	imes 10^{-6} \, F$, $f = 50 \, Hz$, $V_m = 280 \, V$.The angular frequency is $\omega = 2 \pi f = 2 	imes 3.14 	imes 50 = 314 \, rad/s$.Capacitive reactance: $X_C = \frac{1}{\omega C} = \frac{1}{314 	imes 10 	imes 10^{-6}} = \frac{1}{3.14 	imes 10^{-3}} \approx 318.47 \, \Omega$.Inductive reactance: $X_L = \omega L = 314 	imes 6.0 	imes 10^{-6} = 1.884 	imes 10^{-3} \, \Omega$.Impedance of the circuit: $Z = \sqrt{R^2 + (X_C - X_L)^2} = \sqrt{10^2 + (318.47 - 0.001884)^2} \approx \sqrt{100 + (318.47)^2} \approx 318.63 \, \Omega$.$RMS$ voltage: $V_{rms} = \frac{V_m}{\sqrt{2}} = \frac{280}{1.414} \approx 198 \, V$.$RMS$ current: $I_{rms} = \frac{V_{rms}}{Z} = \frac{198}{318.63} \approx 0.621 \, A$.Average power dissipated as heat in the resistor: $P = I_{rms}^2 R = (0.621)^2 	imes 10 = 0.3856 	imes 10 \approx 3.86 \, W$.Rounding to the nearest given option, the power is $3.8 \, W$.

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