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

Step-by-step 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)=(V_(rms))/(Z)\\\\I_(rms)=(82)/(105)\\\\I_(rms)=0.78\ A`

Power is given by :

`P=I_(rms)V_(rms)\cos\phi`

`\cos\phi = (R)/(Z)\\\\\cos\phi = (71)/(105)\\\\\cos\phi =0.676`

Now, power,

`P=0.78* 82* 0.676\\\\P=43.23\ W`

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