Finding i(t) Across R3 & R2 After Switch Closure at t=0

[vthokie11]

Homework Statement

The switch in the circuit has been closed for a long time before opening at t = 0
a. Find i(t) across R3 for t>0.
b. Find i(t) across R2 for t>0.

I have attached the circuit.

Homework Equations

The Attempt at a Solution

The only thing I know for this problem is that when a switch has been in a certain state for a long time an inductor acts essentially like a wire (no resistance) and when the state changes the inductor has infinite resistance.

 

[skeptic2]

To solve this you need to know the formula for di/dt for RL circuits. Isn't this in your textbook or covered by lecture?

 

[vthokie11]

I apologize...I thought that I included the relevant equations...but this is what I know:

What I don't understand is what the change in time is...I really don't know how to go about solving this problem...and I have no examples from lecture...all I have from lecture is basically the 2 equations I have included. Any help would be greatly appreciated...Thanks.

 

[vthokie11]

So I've done some work and this is what I've came up with...I'm not sure if this is even remotely close:

I applied KVL's around each loop

Am I even on the right track with this?

 

[rwisz]

Therefore, when the switch is closed for a long time, the inductor acts like a wire and the current through R3 will be equal to the current through R2. However, without knowing the values of R3 and R2, it is not possible to accurately determine the current through each resistor. It is also important to consider any other components in the circuit and their effects on the current. Further analysis and calculations would be needed to accurately determine i(t) across R3 and R2 for t>0.