Question

A 22.0-mH inductor, with internal resistance of 22.0 Ω, is connected to a 110-V rms source. If the average power dissipated in the circuit is 62.0 W, what is the frequency? (Model the inductor as an ideal inductor in series with a resistor.)

Answer 1

here,

the inductance of inductor , L = 22 mH = 0.022 H

r = 22 ohm

V = 110 V

let the current in the circuit be I

P = I^2 * r

62 = I^2 * 22

solving for I

I = 1.68 A

let the frequency be f

current in the circuit , I = V /sqrt(r^2 + (2*pi*f*L)^2)

1.68 = 110 /sqrt(22^2 + (2*pi*f*0.022)^2)

solving for f

f = 446 Hz

the frequency is 446 Hz