A circuit is constructed with four resistors, one inductor, one battery and a sw

Question

A circuit is constructed with four resistors, one inductor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 40 ?, R3 = 109 ? and R4 = 83 ?. The inductance is L = 551 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?A

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?A

3)

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

4)

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

5)

What is I2(0), the magnitude of the current through the resistor R2 just after the switch is closed?

Explanation / Answer

1) Just after the switch is closed

Inductor will behave as a open circuit.

=> current through the battery , i = V/Req where Req = R1+R2+R3+R4 = 40+40+109+83 = 272 ohm

=> i = 24/272 = 0.0882 A = Current through R1

2) A very long after switch is closed inductor will behave as a short circuit.

=> R3,R2 has no use.

=>  current through the battery , i = V/Req where Req = R1+R4 = 40+83 = 123 ohm

=> i = 24/123 = 0.195 A = current through R1

3) VL(0) = i*(R2+R3) = 0.0882*(40+109) = 13.141 volt

4) IL after very long time

I(L) = i = 0.195 A

5) current through R2(0) = current through R1(0) = 0.0882 A

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