The rms current in an R L circuit is 0.31 A when it is connected to an ac genera

Question

The rms current in an RL circuit is 0.31A when it is connected to an ac generator with a frequency of 50Hz and an rms voltage of 35V .

A.Given that the inductor has an inductance of 165 mH, what is the resistance of the resistor?

B. Find the rms voltage across the resistor.

The rms current in an RL circuit is 0.31A when it is connected to an ac generator with a frequency of 50Hz and an rms voltage of 35V . Given that the inductor has an inductance of 165 mH, what is the resistance of the resistor? Find the rms voltage across the resistor. Find the rms voltage across the inductor.

Explanation / Answer

a)

impedance

Z=Vrms/Irms =35/0.31

Z=112.9 ohms

Inductive reactance

XL=2pifL=2pi*50*165*10^-3

XL=51.84 ohms

impedance

Z=sqrt[R^2+XL^2]

R=sqrt[Z^2-XL^2] =sqrt[112.9^2-51.84^2]

R=100.3 ohms

b)

Vrms=R*Irms =100.3*0.31

Vrms =31.1 V

c)

VL=Irms*XL =0.31*51.84

VL=16.07 V

d)

sqrt[VL^2+Vr^2] =sqrt[31.1^2+16.07^2] =35 V

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