When an inductor of inductance L = frac{6}{pi | vedclass

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(C) Given: $L = \frac{6}{\pi} \ H$, $C = \frac{50}{\pi} \ \mu F = \frac{50}{\pi} 	imes 10^{-6} \ F$, $V_{rms} = 220 \ V$, $f = 50 \ Hz$, $I_{rms} = 4

Vedclass · Accepted Answer

$A$-(iv), $B$-(i), $C$-(ii), $D$-(iii)

Vedclass · Answer

(C) Given: $L = \frac{6}{\pi} \ H$, $C = \frac{50}{\pi} \ \mu F = \frac{50}{\pi} 	imes 10^{-6} \ F$, $V_{rms} = 220 \ V$, $f = 50 \ Hz$, $I_{rms} = 440 \ mA = 0.44 \ A$.$(A)$ Inductive reactance: $X_L = 2 \pi f L = 2 \pi 	imes 50 	imes \frac{6}{\pi} = 600 \ \Omega$.$(B)$ Capacitive reactance: $X_C = \frac{1}{2 \pi f C} = \frac{1}{2 \pi 	imes 50 	imes (\frac{50}{\pi} 	imes 10^{-6})} = \frac{1}{5000 	imes 10^{-6}} = \frac{10^6}{5000} = 200 \ \Omega$.$(D)$ Impedance: $Z = \frac{V_{rms}}{I_{rms}} = \frac{220}{0.44} = 500 \ \Omega$.$(C)$ Resistance: $Z^2 = R^2 + (X_L - X_C)^2 \Rightarrow 500^2 = R^2 + (600 - 200)^2 \Rightarrow 250000 = R^2 + 160000 \Rightarrow R^2 = 90000 \Rightarrow R = 300 \ \Omega$.Thus, $A-(iv), B-(i), C-(ii), D-(iii)$.

List-$I$	List-$II$
$(A) \ X_L$	$(i) \ 200 \ \Omega$
$(B) \ X_C$	$(ii) \ 300 \ \Omega$
$(C) \ R$	$(iii) \ 500 \ \Omega$
$(D) \ Z$	$(iv) \ 600 \ \Omega$

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