Question

In series LCR circuit, resistance is 18 \( \Omega \) and impedance is 33 \( \Omega \). An r.m.s. voltage of 220 V is applied across the circuit. The true power consumed in a.c. circuit is

• A. 400 V
• B. 600 V
• C. 800 V
• D. 200 V

Hint:

In an LCR circuit, the true power is calculated using the voltage, current, and power factor (which is the cosine of the phase angle).

Answer 1

The Correct Option is C

Step 1: Understanding power in an LCR circuit.
The true power consumed in an LCR circuit is given by: \[ P = V_{\text{rms}} I_{\text{rms}} \cos \phi \] where \( \phi \) is the phase angle between the voltage and current. The impedance \( Z \) is related to the resistance \( R \) and reactance \( X \) by: \[ Z = \sqrt{R^2 + X^2} \] The current is given by: \[ I_{\text{rms}} = \frac{V_{\text{rms}}}{Z} \] The power factor is \( \cos \phi = \frac{R}{Z} \). Step 2: Calculating the true power.
Substituting the given values: \[ I_{\text{rms}} = \frac{220}{33} = 6.67 \, \text{A} \] The power factor is: \[ \cos \phi = \frac{18}{33} = 0.545 \] Thus, the true power is: \[ P = 220 \times 6.67 \times 0.545 = 800 \, \text{W} \] Step 3: Conclusion.
Thus, the correct answer is (C) 800 V.