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(C) Given voltage $V = 20 \cos (2000 t)$,comparing with $V = V_0 \cos (\omega t)$,we get peak voltage $V_0 = 20 	ext{ V}$ and angular frequency $\ome

Vedclass · Accepted Answer

$15 \Omega, \frac{2 \sqrt{2}}{3} 	ext{ A}$

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(C) Given voltage $V = 20 \cos (2000 t)$,comparing with $V = V_0 \cos (\omega t)$,we get peak voltage $V_0 = 20 	ext{ V}$ and angular frequency $\omega = 2000 	ext{ rad/s}$.From the circuit,total resistance $R = 10 \Omega + 5 \Omega = 15 \Omega$,inductance $L = 5 	ext{ mH} = 5 	imes 10^{-3} 	ext{ H}$,and capacitance $C = 50 \mu	ext{F} = 50 	imes 10^{-6} 	ext{ F}$.Inductive reactance $X_L = \omega L = 2000 	imes 5 	imes 10^{-3} = 10 \Omega$.Capacitive reactance $X_C = \frac{1}{\omega C} = \frac{1}{2000 	imes 50 	imes 10^{-6}} = \frac{1}{0.1} = 10 \Omega$.Since $X_L = X_C$,the circuit is in resonance,and the impedance $Z = R = 15 \Omega$.The peak current $I_0 = \frac{V_0}{Z} = \frac{20}{15} = \frac{4}{3} 	ext{ A}$.The r.m.s. current $I_{rms} = \frac{I_0}{\sqrt{2}} = \frac{4/3}{\sqrt{2}} = \frac{2 \sqrt{2}}{3} 	ext{ A}$.

In the circuit shown in the figure,an a.c. source gives voltage $V = 20 \cos (2000 t)$. The impedance and r.m.s. current respectively will be:

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