1.What is t 1 , the first time after t = 0 when the magnitude of the voltage acr

Question

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?

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

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as -va-b- Emsinat, where Em-120 V and = 714 radians/ second. The values for the remaining circuit components are: R = 147 , C = 554 ur. The value for L is unkown. What is known is that the voltage across the generator leads the current in the circuit by -31 degrees. E sin(ot

Explanation / Answer

(a)

t=2*pi/w= 2*(3,14)/714= 0,0087 s

w=1/(LC) ^0,5

L= 1/(C*w^2) = 1/(554*10 ^-6  * 714^2) = 3.5 mH

(b) Z = ( R^ 2 + ( L 1 / ( C ) ) ^2)

Z = (147 ^2 + ( 714* 3.5*10 ^-3 1 / ( 714* 554*10 ^-6 ) ) ^2)

Z= 146.95

(c)

Irms=Vrms/R= 120/147= 0,816 A

Imax=Irms/(2 ^0,5)= 0,577 A

Vl(max) = Imax*XL

XL=w*L= 714*3.5*10^0-3= 2.499 ohm

Vmax=  0,577 A * 2.499 ohm = 1,441 V

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