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 = 69 , R3 = 58 and R4 = 98 . The inductance is L = 487 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 Submit

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 Submit

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

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

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

Explanation / Answer

Here,

1) when the switch is just clsoed ,

inductor will behave as open circuit

i1(0) = V/(R1 + R2 + R3 + R4)

i1(0) = 24/(98 + 58 + 69 + 69)

i1(0) = 0.082 A

2)

after a very long time

indutor is short circuited

I1() = V/(R1 +R4)

I1() = 24/(69 + 98)

I1() = 0.144 A

3)

as the inductor is short circuited

VL(0) = V(R2) + V(R3)

VL(0) = (69 + 58) * i1(0)

VL(0) = (69 + 58) * 0.082

VL(0) = 10.41 V

4)

IL() = current through R1 at infnite

IL() = 0.144 A

5)

just after closing the swtich

inductor will behave as open circuit

i2(0) = i1(0)

i2(0) = 0.082 A

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