How to calculate time constant in RC circuit

  • Engineering
  • Thread starter Bromio
  • Start date
  • #1
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Hello.

Homework Statement


Calculate the time response, Vc(t), of the circuit shown in the attached image. Not use Laplace transforms.

Homework Equations


I know that tau = RC in a typical RC circuit.

In general, Vc(t) = {V0 - Vf}*exp(-t/tau) + Vf, where V0 is initial voltage and Vf is final voltage.


The Attempt at a Solution


Once charged, the capacitor behaves like a short-circuit, so I can calculate that Vf = 2,5 V. In addition, V0 = 0 V. So, I only need to know the value of tau. How could I calculate it without using Laplace transforms?

Thank you.
 

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Answers and Replies

  • #2
lewando
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Once charged, the capacitor behaves like a short-circuit
Actually, when a capacitor is charged, no more current flows through it so it acts like an open circuit.

How could I calculate [tau] without using Laplace transforms?
General procedure: remove sources from the circuit by shorting any voltage sources and opening any current sources. Then find Req as it would appear across the capacitor terminal (tau = CReq).
 
  • #3
vela
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Do you know about Thevenin equivalent circuits? Lewando's suggestion follows from finding the Thevenin equivalent of what's connected to the capacitor.
 
  • #4
NascentOxygen
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Assume currents i1, i2, etc., in the various branches, and determine the node voltages. The voltage across the capacitor is 1/C*(integral of i).dt
You should find capacitor current i = Re.Vs

The voltage as a function of time is obtained by solving the first order differential equation. The time constant of the exponential in the time response is Re*C

* I used Re to represent the term by which you divide Vs. The term has units of resistance and it appears in the calculations when you are determining capacitor current.
 
  • #5
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Thank you.

I've just solved the problem: Vc(t) = 2.5(1-exp(-200t))u(t).
 
  • #6
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Isn't the equivalent resistance is 5kohm?
 
  • #7
gneill
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Isn't the equivalent resistance is 5kohm?

Can you show your calculation?
 

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