Nodal Analysis with power supplied to capacitor

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Homework Help Overview

The discussion revolves around a circuit analysis problem involving a capacitor and an inductor, with given values for voltage and resistances. Participants are tasked with determining the inductor current and capacitor voltage, as well as the power supplied by the source before a switch is opened.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply nodal analysis using KCL and expresses uncertainty about the correctness of their results. Some participants question the interpretation of nodes and the treatment of the capacitor and inductor under steady-state conditions. Others suggest considering the behavior of these components in a DC circuit to simplify the analysis.

Discussion Status

There is ongoing dialogue regarding the validity of the original poster's calculations. Some participants have provided hints and guidance on how to approach the problem, emphasizing the importance of understanding the steady-state behavior of capacitors and inductors. Multiple interpretations of the circuit setup are being explored, and participants are encouraged to clarify their reasoning.

Contextual Notes

Participants are discussing the implications of steady-state conditions for capacitors and inductors, which may affect the circuit analysis. There is a focus on ensuring that the assumptions made about the circuit components are accurate before proceeding with calculations.

eatamon
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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
 

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No, your results are not correct. Not sure what "I attempted to treat the load plus the capacitor as one node" means.
 
lewando said:
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.
 
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?
 
Vc=30v right? how would I find the inductor current?
 
Not right. What method or equations did you use to arrive at that wrong answer.
 
lewando said:
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.
 
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: VC will be the same as VR2 and IL will be the same as IR3. After answering this question, what do you get for a simplified circuit?

You could find Req and use the current divider rule to find IL 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.
 

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