A. What is the current i 1 just after S is closed? B. What is the current i 2 ju

Question

A. What is the current i1 just after S is closed?

B. What is the current i2 just after S is closed?

C. What is the current i3 just after S is closed?

D. What is i1 after S has been closed a long time?

E. What is i2 after S has been closed a long time?

F. What is i3 after S has been closed a long time?

G. Apply Kirchhoffs rules to the circuit and obtain a differential equation for i3(t). Integrate the equation to obtain an equation for i3 as a function of the time t that has elapsed since S was closed.

H. Use the equation that you derived in part G to calculate the value of t for which i3 has half of the final value that you calculated in part F.

I. When i3 has half of its final value, what is i2?

J. When i3 has half of its final value, what is i1?

Explanation / Answer

just after closing switch, there will be no current in inductor.

hence i3 = 0   and i1 = i2 = e / (R1+ R2)

A. i1 = 48 / (8 + 5) = 3.7 A

B. i2 = i1 = 3.7 A

C. i3 = 0

D. after very lont time, almost all current will pass through inductor.

hence i2 is aprroax zero.

i1 = i3 = e / R1

i1 = 48 / 8 = 6 A

E. i2 = 0

F. i3 = i1 = 6 A

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