(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

"The switch in the circuit in the figure has been closed for a long time and is opened att= 0. Findi(50 ms)."

I attached an image of the circuit below.

2. Relevant equations

KVL:

Ri + q(t)/C - q(0)/C + vc(t) + Li' = vs(t)

Li'' + Ri' + i/C = vs'(t)

Where vc is voltage across the capacitor and vs is the source voltage. Q is the charge flowing through the current.

3. The attempt at a solution

First I found i(t) through the inductor and the vc prior to the switch opening:

30 = 10i --> i = 3 A

20-vc = 5i --> vc = 5 V

Now, I applied the second equation and this is where I become confused. It has to do with the application of Kirchhoff's Voltage Law. i goes through the bottom of the capacitor, so I don't know how to set up the equation.

Li'' + Ri' + i/C = 0

i'' + 10i' + 25i = 0 This?

i'' + 10i' - 25i = 0 Or this?

Likewise, I'll need to find i'(0) after. Would that be:

Ri + q(t)/C - q(0)/C + vc(t) + Li' = vs(t)

10 + 5 + i' = 10 This?

10 - 5 + i' = 10 Or this?

I think it should be minus in both cases, but the numbers behave weirdly when I try that.

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# Homework Help: Current Through an Inductor

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