Question

An L-R-C series circuit, R = 160 Ω , L = 0.790 H , and C = 1.30×10−2 μF . The source has a voltage amplitude of 140 V and a frequency equal to the resonance frequency of the circuit. A)What is the power factor? B)What is the average power delivered by the source? Express your answer using two significant figures. C) The capacitor is replaced by one with a capacitance of C=3.20×10−2 μF and the source frequency is adjusted to the new resonance value. Then what is the average power delivered by the source? Express your answer using two significant figures.

Answer 1

Answer: a) 1 b) 61 W c) 61 W

Explanation:

a) The  Power Factor (also known as cos φ), is defined by the difference in phase between current and voltage, in a RLC series circuit, and is expressed as follows:

cos φ = R / Z = R / $\sqrt{(R)^{2} + (Xl -Xc)^{2} }$

In resonance, XL =XC, so the circuit behaves like it were purely resistive, so Z=R.

Replacing in the expression for power factor, we have:

cos φ = R/Z = R/R = 1

This means that in resonance, current and voltage are in phase each other.

b) The average power delivered by the source, in resonance, is simply the power dissipated at the resistance R, as follows:

Pavg = V² rms / R = V₀² / √2 / R = 61 W

c) If the circuit remains in resonance, the average power , which does not depends on frequency provided this condition remains, keeps the same, i.e. , 61 W.