How to calculate time constant in RC circuit

[Bromio]

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.

 

[lewando]

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 R_eq as it would appear across the capacitor terminal (tau = CR_eq).

 

[vela]

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

 

[NascentOxygen]

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 = R_e.V_s

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 R_e*C

* I used R_e to represent the term by which you divide V_s. The term has units of resistance and it appears in the calculations when you are determining capacitor current.

 

[Bromio]

Thank you.

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

 

[wstclyq]

Isn't the equivalent resistance is 5kohm?

 

[gneill]

Isn't the equivalent resistance is 5kohm?

Can you show your calculation?