The rms current in an RL circuit is 0.27 A when it is connected to an ac generat

Question

The rms current in an RL circuit is 0.27 A when it is connected to an ac generator with a frequency of 60.0 Hz and an rms voltage of 25 V.
(a) Given that the inductor has an inductance of 130 mH, what is the resistance of the resistor?
?

(b) Find the rms voltage across the resistor.
V

(c) Find the rms voltage across the inductor.
V

(d) In this part you will use your results from parts (b) and (c) to show that

Vrms, R2 + Vrms, L2
is equal to 25 V. First, calculate the squares of the individual rms voltages.
(Vrms,R)2 = V
(Vrms,L)2 = V

Next, calculate the sum of the squares of the voltages.
V2

Finally, calculate the square root of the sum of the squares.
V

Explanation / Answer

Part A)

Starting with V = IZ, we can find Z

(25) = (.27)Z

Z = 92.6

Z = (R2 + XL2)

XL = 2fL = (2)(60)(.130) = 49

R = [(92.6)2 - (49)2]

R = 78.6

Part B)

VR = IR = (.27)(78.6) = 21.2 V

Part C)

VL = IXL = (.27)(49) = 13.2 V

Part D)

V = [(21.2)2 + (13.2)2] = 25V

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