An inductor of 10 text{ mH}, capacitor of 0.1 | vedclass

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(B) The power factor is given by $\cos \phi = \frac{R}{Z} = 0.5$.Since $R = 100 	ext{ } \Omega$, we have $Z = \frac{R}{0.5} = \frac{100}{0.5} = 200 \

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(B) The power factor is given by $\cos \phi = \frac{R}{Z} = 0.5$.Since $R = 100 	ext{ } \Omega$, we have $Z = \frac{R}{0.5} = \frac{100}{0.5} = 200 	ext{ } \Omega$.The impedance of an $LCR$ series circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Squaring both sides, $Z^2 = R^2 + (X_L - X_C)^2$.Substituting the values, $200^2 = 100^2 + (X_L - X_C)^2$.$40000 = 10000 + (X_L - X_C)^2$.$(X_L - X_C)^2 = 30000$.$|X_L - X_C| = \sqrt{30000} = 100\sqrt{3} 	ext{ } \Omega$.Given that the difference is $\sqrt{3}\alpha 	ext{ } \Omega$, we equate $\sqrt{3}\alpha = 100\sqrt{3}$.Therefore, $\alpha = 100$.

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