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 = 51 ?, R3 = 112 ? and R4 = 158 ?. The inductance is L = 385 mH and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.

1) After the switch has been closed for a very long time, it is then opened. What is I3(topen), the current through the resistor R3 at a time topen = 6.4 ms after the switch was opened? The positive direction for the current is indicated in the figure. THE ANSWER IS NOT .0083A

2) What is VL,max(open), the magnitude of the maximum voltage across the inductor during the time when the switch is open? THE ANSWER IS NOT 0.

Explanation / Answer

1)after switch has been closed for a long time we can treat the inductor as a normal conducting wire so we replace the inductor with a conducting wire

appying kirchoffs law on both the loops we get the following equations:

I=I3+IL

KVL in small loop gives

209I+112I3=12

KVL in big loop gives

260I-51I3=12 ( this equation is formed by replacing IL=I-I3)

solving we get I3=0.033A

this current is through R3 when switch is closed

after switch is opened, we have to use decay current formula which is

I=I0exp(-t/tL)

where tL=L/Req is the inductive time constant=1.57x10-3s

putting I0=I3=0.033A and t=6.4x10-3s

we get I3(open)=5.6x10-4A

2) max inductor voltage after switch is open can be found by applying KVL over the right loop

VL=4.56V

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