A circuit is constructed with an AC generator, a resistor, capacitor and inducto

Question

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as = Va - Vb = msint, where m = 120 V and = 524 radians/second. The values for the remaining circuit components are: R = 57 , C = 569 F. The value for L is unkown. What is known is that the voltage across the generator leads the current in the circuit by = 56 degrees.

1)

What is t1, the first time after t = 0 when the magnitude of the voltage across the inductor is maximum?

2)

What is Z, the impedance of the circuit?

3)

What is L, the value of the inductor?

4)

What is VL,max, the magnitude of the maximum voltage across the inductor?

5)

What is VL = Vb - Vc, the voltage across the inductor, at time t = 0? Note that VL is a signed number.

Explanation / Answer

1)

T = angular displacement / omega

phy = 56 deg

convert in radian

phy = 56 * pie / 180

T = (56 * pie) / (180 * 524)

T = 0.001865 sec

2)

cos(phy) = R/Z

Z = R / cos(phy)

Z = 57 / cos56

Z = 101.93 ohm

3)

Xl = w * L

Xc = 1 / w*c

tan(phy) = (Xl - Xc) / R

Xl - Xc = R * tan(phy)

L * w = R * tan(phy) + 1 / wc

L = (57 * tan(56) + 1 / (569 * 10^-6 * 524) ) * (1 / 524)

L = 167.67 mH

4)

by using ohms law

VL(max) = Imax * Xl

VL(max) = Imax * L * w

VL(max) = (Em / Z) * L * w ................................. Imax = Em / Z

= (120 / 101.93) * 0.16767 * 524

VL(max) = 103.43 V

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