Question

In series LCR circuit $R=18\Omega$ and impedance is $33\Omega$. An r.m.s. voltage $220V$ is applied across the circuit. The true power consumed in a.c. circuit is

• A. $200W$
• B. $400W$
• C. $600W$
• D. $800W$

Answer 1

Answer: (B)

$400W$

Given : $V_{rms}=220$ V $R=18\Omega$ $Z=33\Omega$

True power consumed $P=\frac{1}{2}\frac{V_{rms}^2}{Z}\cos \varphi$

where $\cos \varphi =\frac{R}{Z}$

$⟹$ $P=\frac{V_{rms}^{2}R}{2Z^2}$

$\therefore$ $P=\frac{220\times 220\times 18}{2\times {33}^2}$

We get $P=400W$