Hello plz I need solutions with steps A circuit is constructed with four resisto

Question

Hello plz I need solutions with steps

A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 41 ?, R3 = 110 ? and R4 = 84 ?. The inductance is L = 576 mH and the battery voltage is V = 24 V.

1-The switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?

2-What is I1(?), the magnitude of the current that flows through the resistor R1 a very long time after the switch has been closed?

3-What is VL(0), the magnitude of the voltage across the inductor just after the switch is closed?

4-What is IL(?), the magnitude of the current through the inductor after the switch has been closed for a very long time?

Explanation / Answer

1) just after siwtch is closed , inductor will act as open circuit , so current in inductor is zero.

      i1(0) = V/(R1+R2+R3+R4)   = 24/276 =0.0869 A

2) at t = inifnity , inducotr is act as short circuit ,   so current in   R2 = R3 =0

         i1(?) = current in R1 = V /(R1+R4) =24/(41 + 84) =0.192 A

3)   VL(0) = volateg across indcutor =   voltage across   (R2+R3) = i1(0) [ R2 +R3) = 13.1 V

4) IL(?) = current in inductor is same as current in R1 = 0.192 A

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