A series circuit consists of a 50-Hz ac source, a 40-Ω resistor, a 0.30-H inductor, and a 60-μF capacitor. The rms current in the circuit is measured to be 1.6 A. What is the power factor of the circuit?

Question

Physics

Eliana Sutton

18 August, 00:20

A series circuit consists of a 50-Hz ac source, a 40-Ω resistor, a 0.30-H inductor, and a 60-μF capacitor. The rms current in the circuit is measured to be 1.6 A. What is the power factor of the circuit?

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Answers (1)

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Elaine · Answer 1

0.7

Explanation:

f = 50 hz, R = 40 ohm, L = 0.3 h, C = 60 uC = 60 x 10^-6 c

XL = 2 x 3.14 x f x L = 2 x 3.14 x 50 x 0.3 = 94.2 ohm

Xc = 1 / (2 x 3.14 x 50 x 60 x 10^-6) = 53.078 ohm

Impedance is Z.

Z^2 = R^2 + (XL - Xc) ^2

Z^2 = 40^2 + (94.2 - 53.078) ^2

Z^2 = 1600 + 1691.019

Z = 57.37 ohm

The power factor is given by

CosФ = r / Z = 40 / 57.37 = 0.697 = 0.7