Question

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

• A. 7.8 A and 30°
• B. 7.8 A and 45°
• C. 15.6 A and 30°
• D. 15.6 A and 45°

Answer 1

Answer: (B)

7.8 A and 45°

Answer 2

The circuit consists of a resistor, a capacitor, and an inductor connected in series to an AC power supply.

The impedance $Z$ of the series RLC circuit is calculated using:

$$Z = \sqrt{R^2 + (X_L - X_C)^2}$$

Given $R = 20 \, \Omega$, $X_C = 25 \, \Omega$, and $X_L = 45 \, \Omega$, the impedance is:

$$Z = \sqrt{20^2 + (45 - 25)^2} = \sqrt{20^2 + 20^2} = \sqrt{800} = 20\sqrt{2} \, \Omega$$

The RMS current $I_{rms}$ is:

$$I_{rms} = \frac{V_{rms}}{Z} = \frac{220 \, \text{V}}{20\sqrt{2} \, \Omega} = \frac{11}{\sqrt{2}} \, \text{A} \approx 7.8 \, \text{A}$$

The phase angle $\phi$ is:

$$\tan \phi = \frac{X_L - X_C}{R} = \frac{45 - 25}{20} = \frac{20}{20} = 1$$

Thus, $\phi = \tan^{-1}(1) = 45^\circ$.