SHOW ALL WORK 4) Consider the circuit sketched above. The battery has emf of 27

Question

SHOW ALL WORK

4) Consider the circuit sketched above. The battery has emf of 27 volts. The inductance is L = 0.40 H and the resistances are R1 = 12 ? and R2 = 9.0?. Use the figure to answer the following.

A)Initially the switch S is open and no currents flow. Then the switch is closed. What is the current in the resistor R1 just after the switch is closed?

B)After leaving the switch closed for a long time, it is opened again. Just after it is opened, what is the current in R1?

C)After leaving the switch closed for a long time, it is opened again. How long does it take for the current to reach 1/3 of the maximum current.

Explanation / Answer

a) current in Inductor coil can not change instantly,

so just after closing the switch, current in L remains zero.

that means all the current flow from R1.

I = e/R1 = 27/12 = 2.25 A

b) after long time,

Pd across R1 = e = 27 volt.

and PD across L becomes zero.

so curremt through , L and R2 = 27/9 = 3 A

so current through L, will not change instantly.

so current in loop = current in loop = 3 A

c) I = I0 ( e ^ (-tL/R ))

and R = R1 + R2 = 9 + 12 = 21 ohm

1 = 3 (e^(-t / 21))

t = 23.07 sec

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