# RLC circuit problem

1. The problem statement, all variables and given/known data
A series LCR circuit with ##L=0.125/\pi## H, ##C=500/\pi## nF and ##R=23\,\Omega## is connected to a 230 V variable frequency supply. For what reactance of circuit, the power transferred to the circuit is half the power at resonance?

2. Relevant equations

3. The attempt at a solution
At resonance,
$$f=\frac{1}{2\pi\sqrt{LC}}=2000\,Hz$$
Hence, the power transferred at resonance is given by ##P=V^2_{rms}/R=2300\,\,W##.

When the power transferred is half, let the reactance be Z, hence,
$$P’=\frac{V^2_{rms}}{Z}\cos\phi=\frac{V^2_{rms}}{Z}\frac{R}{Z}$$
As per the question:
$$\frac{V^2_{rms}}{Z}\frac{R}{Z}=\frac{1}{2}\times 2300$$
$$\Rightarrow \frac{230\times 230 \times 23}{Z^2}=\frac{1}{2}\times 2300$$
$$\Rightarrow Z=23\sqrt{2} \,\,\Omega$$
But this is incorrect. The correct answer is ##23\,\,\Omega##. :confused:

Any help is appreciated. Thanks!

http://ift.tt/1k1nCNa