Nodal Analysis with power supplied to capacitor

[eatamon]

Homework Statement

Following circuit has v=30v, r1=20ohm,r2=10ohm,r3=15ohm. A)Determine inductor current (I) and capacitor voltage (Vc). B)Determine power supplied by source before switch is open.

Homework Equations

KCL
P=VI

The Attempt at a Solution

I attempted to treat the load plus the capacitor as one node (v3=vc). From there I took V1 to be 30v. I set up two KCL equations and solved for V2 and v3. I got Vc=7.5 v and I=1.5 A. Then for part b, I used P=VI and got 11.25 watts. I just wanted to know of this answer is correct or not. Thanks

 

[eatamon]

Added more details

 

[lewando]

No, your results are not correct. Not sure what "I attempted to treat the load plus the capacitor as one node" means.

 

[eatamon]

No, your results are not correct. Not sure what "I attempted to treat the load plus the capacitor as one node" means.

I assumed that there was no load resistance so the voltage remained the same throughout it.

 

[lewando]

Everything on the RHS of the switch is the "load resistance". Do you recall what a capacitor looks like at steady-state with a DC voltage applied? How about an inductor at steady-state with a DC current going through it?

 

[eatamon]

Vc=30v right? how would I find the inductor current?

 

[lewando]

Not right. What method or equations did you use to arrive at that wrong answer.

 

[eatamon]

Not right. What method or equations did you use to arrive at that wrong answer.

Ive been using several techniques and I don't think any are right. Would finding Req to find the total current be helpful? then use current divider rule to find IL? Can someone please tell me the approach to solve this, it would be very appreciated.

 

[lewando]

It is easier for us to help if you communicate the specifics of the work that you are doing, otherwise it’s hard to know where exactly your thought process is breaking down.

Maybe you missed my question regarding how you are treating capacitors and inductors under steady-state DC conditions. This question still stands. Hint: one of them will have zero current flowing through it and will look like an open circuit (infinite resistance). The other will have zero voltage across it and will look like a short circuit (zero resistance). Applying this knowledge to your circuit simplifies it into a purely resistive network which you can analyze using standard methods. Another hint: V_C will be the same as V_R2 and I_L will be the same as I_R3. After answering this question, what do you get for a simplified circuit?

You could find R_eq and use the current divider rule to find I_L if you like (if you go down this path, please show your steps and intermediate results), but there is another more direct way to get the answer.