# Solving an RC circuit question using Superposition

• Engineering
Hello,

The circuit attached below is from Richard Dorfs Intro to Electric Circuits book. The switch is shut for a long time and opened at t=0.

The question asks to find the i(t) across R11, which they use nodal analaysis and find it to be 66.67 - 16.666 e$$^{-t/120}$$ micro Amps, where 66.67 micro Amps is due to the 8 v source and - 16.666 e$$^{-t/120}$$ source due to the capacitor

My question is that if we use superposition instead, should the current due to the 8 v source and the capacitor be added since both send current towards R11 in the same direction?

Thank you in advance

P.S since this is more a theoretical question, i thought best i post it here other than the Homework section

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## Answers and Replies

Hello,

The circuit attached below is from Richard Dorfs Intro to Electric Circuits book. The switch is shut for a long time and opened at t=0.

The question asks to find the i(t) across R11, which they use nodal analaysis and find it to be 66.67 - 16.666 e$$^{-t/120}$$ micro Amps, where 66.67 micro Amps is due to the 8 v source and - 16.666 e$$^{-t/120}$$ source due to the capacitor

My question is that if we use superposition instead, should the current due to the 8 v source and the capacitor be added since both send current towards R11 in the same direction?

Thank you in advance

P.S since this is more a theoretical question, i thought best i post it here other than the Homework section

First, I think when the switch open, Cap is not going to send current to R11 in the same direction as the 8V battery. Because if you use super position to find the voltage at probe11 when the switch is closed, the voltage is lower than when the switch is open for a long time. The final voltage at this point will be 4V after the switch opened for a long time and let everything settle.

I have not think in detail how to do the calculation, but super position definitely will work. My guess is to treat the cap as a variable voltage source that slowly rise from initial voltage, with the time constant of RC where R = R10 and R11 in parallel and you have to calculate the thev. voltage or something like that to the final voltage of 4V. As I said, I am too lazy to go into the detail, but the answer is yes, you have to include the cap. until the circuit settle.

Last edited:
Yungman

I made a mistake above. The current due to the capacitor is 16.666 eLaTeX Code: ^{-t/120} not - 16.666 eLaTeX Code: ^{-t/120}.

However in the book instead of adding the current....they are subtracting them. This is what i dont get since both currents ( current due to the 8V voltage source and current due to the capacitor) are in the same direction

So shouldnt it be added and hence shouldnt the answer be 66.67 + 16.666 eLaTeX Code: ^{-t/120} and not 66.67 - 16.666 eLaTeX Code: ^{-t/120}

Any help in this regard will be helpful.....Also i dont have the book with me but the answer is correct.