In a simple AC circuit shown, C = 0.015 F, L = 1.5 H, R = 43 O, and I = Imaxsin(

Question

In a simple AC circuit shown, C = 0.015 F, L = 1.5 H, R = 43 O, and I = Imaxsin(?t), where Imax = 6.5 A and ? = 75 rad/s.

Part (e) Express the maximum potential difference between a and b, ?Vab,max, in terms of Imax and XC.

Part (f) Calculate the numerical value of ?Vab,max in volts.

Part (g) Express the maximum potential difference between b and c, ?Vbc,max, in terms of Imax and R.

Part (h) Calculate the numerical value of ?Vbc,max in volts.

Part (i) Express the maximum potential difference between c and d, ?Vcd,max, in terms of Imax and XL.

Explanation / Answer

e)

Vab,max = Imax XC

f)

XC = 1/wC = 1/(75 x 0.015) = 0.889

Vab,max = Imax XC = 6.5 x 0.889 = 5.78 volts

g)

Vbc,max = ImaxR

h)

Vbc,max = ImaxR = 6.5 x 43 = 279.5 ohm

i)

Vcd,max = Imax XL

j)

XL = wL = 75 x 1.5 = 112.5 ohm

Vcd,max = Imax XL = 6.5 x 112.5 = 731.25

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