Question

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

• A. \(400\) W
• B. \(600\) W
• C. \(200\) W
• D. \(800\) W

Hint:

True power = V^2 R / Z^2.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The true (average) power is \(P=V_{rms}I_{rms}\cos\phi\), with \(I_{rms}=\dfrac VZ\) and \(\cos\phi=\dfrac RZ\).

Step 2: Find the current and power factor:
\(I=\dfrac{220}{33}=6.67\) A. \(\cos\phi=\dfrac{18}{33}=0.545\).

Step 3: Compute the power:
\(P=220\times6.67\times0.545=800\) W. Equivalently \(P=I^2R=\left(\dfrac{220}{33}\right)^2\times18=44.44\times18=800\) W. Option D.

Step 4: Why the other options are wrong.
200, 400 and 600 W are not given by any of the above formulas with these values.

Final Answer:
The true power is 800 W. \[ \boxed{\text{(D) }800\ \text{W}} \]