7.19 Suppose the circuit in Exercise 7.18 has a resistance of 15 Ω. Obtain the average power transferred to each element of the circuit, and the total power absorbed.
Here,
Inductance, 𝐿 = 80 mH
Capacitance, 𝐶 = 60 μF
rms voltage 𝑉 = 230 V
Frequency, 𝑓 = 50 Hz
ω=2πf=2π×50Hz=100πrads−1
Resistance, 𝑅𝑅 = 15 Ω
The impedance of the circuit –
Z=√(XL−XC)2+R2=√(100π×80×10−3−1100π×60×10−6)2+152=31.728Ω
Current following in the circuit-
Irms=VZ=230V31.72Ω=7.25A
The average power transferred to the resistor,
PR=I2rmsR=7.252×15=791W
The average power transferred to the resistor and capacitor, PC=PI=0
As the average power transferred to the inductor and the capacitor is zero in one
complete cycle. Hence, the total transferred is 791 W.
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