# Homework Help: Finding current in RC circuit

1. May 8, 2014

### dwn

1. The problem statement, all variables and given/known data

Image

3. The attempt at a solution

I know how to solve for a and c.

a: 300V / (300Ω) = 1 A
c: 120V / (200Ω) = 0.6 A

what I don't understand is how they solved for B (0.6A), considering the current is 3A provided by the capacitor.

I initially tried to use a current divider, but that didn't give me the correct result.
Since the capacitor acts as a voltage source, I considered trying to find the voltage of the capacitor, v = Ve(-t/RC), but the value of C is not given.

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Last edited: May 8, 2014
2. May 8, 2014

3. May 8, 2014

### dwn

Hopefully it will work now.

4. May 8, 2014

### donpacino

Do you know what the 'u' means in the equations?

u is the identifier for unit step function.

if I have an equation X=u(t), that mean X=0 when t<0, and 1 when t>=0

so if iC=3u(-t). iC=3u(-t) when t<=0, and iC=0 when t>0

5. May 8, 2014

### dwn

Yes, I was aware of that. That's how I solved the for a and c. For part b we are to solve for -0.5 second, which means that neither voltage sources are active, and the only source comes from the capacitor (3 amps). Correct?

6. May 8, 2014

### donpacino

so by 'a' you mean you're solving for i1 at t=-1.5?
if that is the case, then your method of solving the problem is incorrect, and you happened to get the correct answer.

at t=-1.5:
Va=0
Vb=0
iC=3
you use current division to find i1
i1=iC*100/(100+200)=1A

same with C:
at t=1.5
vA=300
vB=-120
iC=0

write a kvl
vA-100*i1+vB-200*i1=0
i1=0.6 A

at t=-0.5:
vA=300u(t-1) since t-1=-1.5, vA=0
vB=120(t+1) since t+1=0.5, vB=-120
iC=3u(-t) since -t=0.5, iC=3

.....

7. May 8, 2014

### dwn

Oh wow, I think I was jumping to conclusions and just got lucky. I see the mistake now, thank you very much! Thought I was doing right thing since the answer just happened to work out that way. Wish the textbook wouldn't do that, set's one off in the wrong direction! haha

8. May 8, 2014

### donpacino

you're welcome. Mistakes will always happen. The important thing is to rectify them!