The rms current in an RL circuit is 0.28 A when it is connected to an ac generat

Question

The rms current in an RL circuit is 0.28 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 170 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

a)reactance of inductor=L=64.09

Let the resistance be R

25/sqrt(R2+64.092)=0.28

Solving,

R=62.17

b)Total impedance=sqrt(R2+64.092)=89.3

V=62.17/89.3*25=17.41V

c)V=64.09/89.3*25=17.95V

d)Vrms2=17.412+17.952=625.2V2

V2=252=625V2

Hence proved.

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