Q.50. An inductor of 10 mH, capacitor of 0.1 \mu F and a resistor of 100 \Omega are connected in series across an a.c power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5. The diffe

Question

Q.50. An inductor of 10 mH, capacitor of 0.1 \mu F and a resistor of 100 \Omega are connected in series across an a.c power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacitance reactance is . The value of  is __________.

FirstInTest · Accepted Answer

Correct answer: 100. Given power factor $\cos\phi = 0.5$. This implies $\phi = 60^\circ$.For an RLC series circuit, $	an\phi = \frac{|X_L - X_C|}{R}$.So, $	an 60^\circ = \sqrt{3} = \frac{|X_L - X_C|}{R}$.Given $R = 100 \Omega$.Therefore, $|X_L - X_C| = R\sqrt{3} = 100\sqrt{3} \Omega$.We are given that the difference in reactance is $\sqrt{3}\alpha \Omega$.Comparing $100\sqrt{3} \Omega$ with $\sqrt{3}\alpha \Omega$, we get $\alpha = 100$.

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