# How to calculate time constant in RC circuit

• Engineering
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.

#### Attachments

• RC.png
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lewando
Homework Helper
Gold Member
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).

vela
Staff Emeritus
Homework Helper
Do you know about Thevenin equivalent circuits? Lewando's suggestion follows from finding the Thevenin equivalent of what's connected to the capacitor.

NascentOxygen
Staff Emeritus
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.

Thank you.

I've just solved the problem: Vc(t) = 2.5(1-exp(-200t))u(t).

Isn't the equivalent resistance is 5kohm?

gneill
Mentor
Isn't the equivalent resistance is 5kohm?