First order RC: Find Unknown DC Circuit, given current graph

[iharuyuki]

Homework Statement

Homework Equations

[/B]
Tao = R(th) C

The Attempt at a Solution

The unknown DC circuit model consists of a V(th) and R(th)

Tao = (R(th) + 3000) C , total resistance of circuit is R(th) + 3000
0.004 = (R(th) + 3000) (1x10^-6)
R(th) = 1 kOhm

The V(th) should oppose the known source since i(t) goes to 0.
Doing a KVL around the loop clockwise.

-10V + 3000( I ) + I (1000) + V(th) = 0, Voltage across capacitor is 0 since at t=0 it is like steady state.
also, at t=0, I = 0.001 A
then solving gives V(th) = 6V

I get the hunch that the working is wrong but the answer is right by coincidence. Would the working be correct?

Thank you very much.

 

[BvU]

It's basically correct. The problem statement doesn't explicitly say the capacitor starts out uncharged, but that's a reasonable assumption if nothing else is given.

Your wording "at t=0 it's like steady state" isn't all that clear: steady state is clearly not the case at t=0.
What happens at t=0 follows from a second relevant equation: $Q = CV$ which means that at t=0 the voltage drop over the capacitor is zero (-- provided it's uncharged to begin with!).