# Find the voltage at specific time

Joined Feb 11, 2019
22 Translation: The circuit in the figure closes at t = 0.
What is the voltage, Ux , at t = 1 milliseconds if the capacitor was uncharged at t = 0.

I’m not sure how to solve this problem. I attempted a solution but I think I’m doing something wrong. Last edited by a moderator:

#### wayneh

Joined Sep 9, 2010
16,274
You got off to a bad start. Are R1 and R3 really in parallel to R2?

• #### WBahn

Joined Mar 31, 2012
25,283
You want to determine the Thevenin equivalent circuit as seen by the capacitor. After that it's a simply first order circuit.

• Joined Feb 11, 2019
22
You got off to a bad start. Are R1 and R3 really in parallel to R2?
I think so? Well I would say that the capacitor is parallel to R2 anyways.

Joined Feb 11, 2019
22
You want to determine the Thevenin equivalent circuit as seen by the capacitor. After that it's a simply first order circuit.
Ok thanks I will look in to it Joined Feb 11, 2019
22
You got off to a bad start. Are R1 and R3 really in parallel to R2?
If they are not parallell, and not in series, what is the relationship? #### crutschow

Joined Mar 14, 2008
24,402
The resistors are in series.
The capacitor is in parallel with R2.
So first you find the equivalent resistance at each of the capacitors terminals (assume the voltage source looks like a short), and the DC voltage at each capacitor terminal.
That gives you a Thevenin equivalent circuit.
From that you have the RC time constant and can calculate the response.

• #### Jony130

Joined Feb 17, 2009
5,145
If they are not parallell, and not in series, what is the relationship?
Well I think you got that part right Rth is equal to (R1+R3)||R2 ≈ 762Ω and that the capacitor will charge from 0V to 1.19V at 5*Rth*C
You even got the 0.73 part right. But you made an error in your final step.

#### Jony130

Joined Feb 17, 2009
5,145
Also notice that the Vx voltage will change from Vx =3.4357V (at t = 0) to 3.8V (at t =∞), only by 0.372V

Joined Feb 11, 2019
22
Also notice that the Vx voltage will change from Vx =3.4357V (at t = 0) to 3.8V (at t =∞), only by 0.372V
How did you get Vx to 3.4357V at t = 0 ? Joined Feb 11, 2019
22
My thevenin circuit looks like this: The voltage for Ux at t = 0.001s should be 3.71.

How can I get that answer with this formula?

Vc = V(1-e^(-t/RC))

#### WBahn

Joined Mar 31, 2012
25,283
How is the voltage going to go above your 1.19 V source?

Where did that answer come from?

What do you get for your time constant?

How many time constants is 1 ms?

#### MrAl

Joined Jun 17, 2014
7,179
Hi,

Good question, and interestingly i got a similar answer i wont spell out just yet.
So how did he get that.

Joined Feb 11, 2019
22
How is the voltage going to go above your 1.19 V source?

Where did that answer come from?

What do you get for your time constant?

How many time constants is 1 ms?
The answer should be correct, got it from the same book as this exercise. 3.71V

Time constant: 762 * 1 * 10^-6 = 7.62 * 10^-4

#### Jony130

Joined Feb 17, 2009
5,145
How did you get Vx to 3.4375V at t = 0 ?
At time t = 0 you have an empty capacitor with Vc = 0V, which means that exactly at this moment of time you can replace the capacitor with a short circuit.
Try it, and you will see that Vx = 3.4375V

• Joined Feb 11, 2019
22
Hi,

Good question, and interestingly i got a similar answer i wont spell out just yet.
So how did he get that.
Please do if you got time Like I said the textbook said 3.71 at t= 0.001s so should be correct

#### Jony130

Joined Feb 17, 2009
5,145
Like I said the textbook said 3.71 at t= 0.001s so should be correct
I've got the same answer. And as I said early you got all the information needed to solve it.

Joined Feb 11, 2019
22
I've got the same answer. And as I said early you got all the information needed to solve it.
Me very dumb. Could you show me how you did it? I don't get it. :/

#### Jony130

Joined Feb 17, 2009
5,145
This question is tricky because the capacitor is not connected to the reference point (GND) but Vx is.
Vx change from Vx =3.4357V (at t = 0) to 3.8V (at t =∞), only by 0.372V.
And the voltage across R3 resistor is changing form 3.4375V to 2.62V, drops by 0.8175V.
Also notice that 0.372V + 0.8175V ≈ 1.19V
But you shoud care only about Vx change ( ΔVx = 0.372V)

• • 