Q.50. An inductor of 10 mH, capacitor of 0.1 \mu F and a resistor of 100 \Omega are connected in ser

Q: What is the correct answer for this exam Physics Q50?

The correct answer is 100. Given power factor $\cos\phi = 0.5$. This implies $\phi = 60^\circ$.For an RLC series circuit, $\tan\phi = \frac{|X_L - X_C|}{R}$.So, $\tan 60^\circ = \sqrt{3} = \frac{|X_L - X_C|}{R}$.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 $\sqrt{3}\alpha \Omega$,

Q: 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…

The correct answer is 100. Given power factor $\cos\phi = 0.5$. This implies $\phi = 60^\circ$.For an RLC series circuit, $\tan\phi = \frac{|X_L - X_C|}{R}$.So, $\tan 60^\circ = \sqrt{3} = \frac{|X_L - X_C|}{R}$.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 $\sqrt{3}\alpha \Omega$,

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

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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