Question

An L-R-C series circuit is connected to a 120 Hz ac source that has Vrms = 82.0 V. The circuit has a resistance of 71.0 Ω and an impedance at this frequency of 107 Ω and an impedance at this frequency of 105Ω. What average power is delivered to the circuit by the source?

Answer 1

Explanation:

Given that,

Frequency of LCR circuit is 120 Hz

RMS voltage, $V_{rms}=82\ V$

Resistance of circuit, R = 71 Ω

Impedance, Z = 107 Ω

We need to find the average power is delivered to the circuit by the source. Firstly, finding the rms value of current,

$I_{rms}=\dfrac{V_{rms}}{Z}\\\\I_{rms}=\dfrac{82}{105}\\\\I_{rms}=0.78\ A$

Power is given by :

$P=I_{rms}V_{rms}\cos\phi$

$\cos\phi = \dfrac{R}{Z}\\\\\cos\phi = \dfrac{71}{105}\\\\\cos\phi =0.676$

Now, power,

$P=0.78\times 82\times 0.676\\\\P=43.23\ W$

So, the average power of 43.23 watts is delivered to the circuit by the source.