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 = 49 , R3 = 107 and R4 = 146 . The inductance is L = 362 mH and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.

1)

The switch has been open for a long time when at time t = 0, the switch is closed. What is I4(0), the magnitude of the current through the resistor R4 just after the switch is closed?

A

2)

What is I4(), the magnitude of the current through the resistor R4 after the switch has been closed for a very long time?

A

3)

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

A

4)

What is VL,max(closed), the magnitude of the maximum voltage across the inductor during the time when the switch is closed?

V

Explanation / Answer

part a )

at t = 0

no current in R2

I4 = V/R1+R3+R4

I4 = 0.0397 A

part 2 )

after a long time R2 and R3 in parallel

R23 = R2*R3/(R2+R3)

I4 = V/R1+R4+R23

I4 = 0.05249 A

part 3 )

V23 = I*R23

V23 = 1.764 V

since R2 and R3 in parallel so voltage remain same

V2 = V3

V2 = I2*R2

I2 is the current in inductor

IL = V2/R2 = 0.036 A

part 4 )

V = 0.0397 * R3 = 4.25 V

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