Calculate voltage over capacitor and resistance

[Sailhill]

Homework Statement

The task is to calculate the voltage over a capacitor and resistance after 1.0 ms. (Ux) if the capacitor had no charge before the switch was closed.

Relevant Equations

Vs=Vc*(1-exp((-t)/(R*C)))

Hi! I tried by using the Thevenin. Later using Vth and Rth to calculate Vs(0.1ms).
After that I divided the voltage from E over R1 and R3.

The circuit and my attempt:

 

[kuruman]

Is there a question you wish to ask? The numbers you put down are useless without units attached to them.

 

[DaveE]

1) What is your question?
2) Check your value for Vth. I found something different. If you think you were correct, please describe your method.
3) Your result for the exponential calculation used 1msec, but your notes say 10msec.
4) Personally, I very much prefer to use a scientific or engineering notation, like 1⋅10^-6 instead of 0.000001. I HATE counting long strings of zeros; I often screw it up and have little confidence in my accuracy.

In general it looks to me like you need to slow down a bit and don't skip steps. It just seems a bit sloppy to me.

 

[kuruman]

I HATE counting long strings of zeros;

Amen, brother. In this particular problem time $t$ is given in ms so it would be expedient to convert the time constant to ms before substituting. That is one of the many reasons why putting down units is important.

 

[Sailhill]

1) What is your question?
2) Check your value for Vth. I found something different. If you think you were correct, please describe your method.
3) Your result for the exponential calculation used 1msec, but your notes say 10msec.
4) Personally, I very much prefer to use a scientific or engineering notation, like 1⋅10^-6 instead of 0.000001. I HATE counting long strings of zeros; I often screw it up and have little confidence in my accuracy.

In general it looks to me like you need to slow down a bit and don't skip steps. It just seems a bit sloppy to me.

1) The question in the task is: "What is the voltage across capacitor Ux 1ms after the switch "S" is closed?"
The capacitor is initially uncharged. I'm having difficulty obtaining the correct answer and identifying my mistake.
2) I recalculated and now obtained the Thevenin voltage (Vth) as 1.1905 V.
3) Ah, that was an error. The time should indeed be 1 ms.
4) Sorry for the messy notes. I re did the calculation, trying to keep it clearer.

I believe I've correctly determined the Thevenin equivalent now. However, my main challenge lies in calculating Vc and integrating it with Vs. I'm uncertain about the accuracy of my method in calculating Vs and Vc separately and then combining them. I wrote in the notes from what part I am uncertain.

 

[kuruman]

I agree with your answer that the voltage across the capacitor and resistor R2 at t = 1 ms is 0.87 V. Isn't that what you had to find? I don't understand what you mean by (Ux). If this problem is originally in a non-English language, try https://translate.google.com/ and post the translation it gives you.

 

[DaveE]

However, my main challenge lies in calculating Vc and integrating it with Vs.

Are you asking how the exponential response formula $V_c = V_s (1-e^{ \frac{-t}{\tau}})$ is derived?
If so, have you studied calculus and simple differential equations yet?

You will need to solve for the currents, mostly through R1. Then use KVL to determine the voltage U_x.

 

[Sailhill]

Thanks for the help! I used KVL and got the correct answer, much appreciated

Vs - (R1*I) - Vc - (R3*I)=0
I=1.29 mA
VR3=I * R3
VR3=1.29 mA * 2.2k Ohm, (VR3: voltage over R3)
Ux=VR3 + Vc
Ux=3.71 V