An inductor with inductance L = 0.400 H and negligible resistance is connected t

Question

An inductor with inductance L = 0.400 H and negligible resistance is connected to a battery, a switch S , and two resistors, R1 = 5.00 and R2 = 6.00 (Figure 1) . The battery has emf 48.0 V and negligible internal resistance. S is closed at t=0.

A) What is the current i1 just after S is closed? Express your answer with the appropriate units.

B) What is the current i2 just after S is closed? Express your answer with the appropriate units.

C) What is the current i3 just after S is closed? Express your answer with the appropriate units.

D) What is i1 after S has been closed a long time? Express your answer with the appropriate units.

E) What is i2 after S has been closed a long time? Express your answer with the appropriate units.

F) What is i3 after S has been closed a long time? Express your answer with the appropriate units.

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. Express your answer in terms of the variables  R1, R2, L, E.

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. Express your answer with the appropriate units.

I) When i3 has half of its final value, what is i2? Express your answer with the appropriate units.

J) When i3 has half of its final value, what is i1? Express your answer with the appropriate units.

Explanation / Answer

a)

Immediately after switch is closed at t=0 inductor acts as open circuit

I1=E/(R1+R2) =48/(5+6)

I1=4.36 A

b)

I2=I1=4.36 A

c)

IL=0 A

d)

After long time switch is closed inductor acts as short circuit ,therefore

I1=E/R1=48/5 =9.6 A

e)

I2=0 A

f)

I3=I1=9.6 A

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