The rms current in an RL circuit is 0.22 A when it is connected to an ac generat

Question

The rms current in an RL circuit is 0.22 A when it is connected to an ac generator with a frequency of 60.0 Hz and an rms voltage of 25 V. Given that the inductor has an inductance of 120 mH, what is the resistance of the resistor? Find the rms voltage across the resistor. Find the rms voltage across the inductor. In this part you will use your results from parts (b) and (c) to show that square root V_rms, R^2 + V_rms, L^2 is equal to 25 v- First, calculate the squares of the individual rms voltages. Next, calculate the sum of the squares of the voltages. Finally, calculate the square root of the sum of the squares.

Explanation / Answer

z = V/I

z = 25/0.22

z = 113.636

z^2 = XL^2 + R^2

XL = 2pif*L = 45.24

R = sqrt(z^2 - XL^2)

R = 104.24 ohm

part b )

Vrms = Irms * R

Vrms = 22.93 V

part c )

Vrms = Irms * XL

Vrms = 9.9528

part d )

Vrms,R^2 = 525.7849

Vrms , L^2 = 99.05822784

sum = 624.8431278

square root = 24.99686 = 25

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