To an AC power supply of 220 V at 50 Hz, a resistor of 20 ω, a capacitor of reactance 25 ω and an inductor of reactance 45 ω are…

Question

To an AC power supply of 220 V at 50 Hz, a resistor of 20 ω, a capacitor of reactance 25 ω and an inductor of reactance 45 ω are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage are, respectively:

1. A. 7.8 A and 30°
2. B. 7.8 A and 45° (Correct answer)
3. C. 15.6 A and 30°
4. D. 15.6 A and 45°

Correct Answer

Option B — 7.8 A and 45°

Detailed Solution & Explanation

The correct answer is 7.8 A and 45°.

Key Points

• Impedance: $Z=\sqrt{(X_L-X_C)^2+R^2}=\sqrt{(45-25)^2+20^2}=\sqrt{20^2+20^2}=20\sqrt2\,\Omega$.
• Current: $I=\dfrac{V}{Z}=\dfrac{220}{20\sqrt2}=\dfrac{11}{\sqrt2}\approx 7.8$ A.
• Phase angle: $\tan\phi=\dfrac{X_L-X_C}{R}=\dfrac{45-25}{20}=1\Rightarrow \phi=45^\circ$.