What is the voltage across a capacitor?

Discussion in 'Homework Help' started by charmcaster, Jan 28, 2015.

1. charmcaster Thread Starter New Member

Jan 13, 2015
22
0
What is the voltage across a capacitor after being charged from a 100 V source for a period of one time constant?

2. wmodavis Well-Known Member

Oct 23, 2010
739
150
There is a formula for that. Do you know what it is?

A key piece of information that will help you is the definition of Time Constant.

3. charmcaster Thread Starter New Member

Jan 13, 2015
22
0
I google n get, after the first interval, the capacitor voltage equals 63.2% of the battery voltage. so answer I got is 63.2. Is it right?

Oct 23, 2010
739
150
Yup.

Jan 13, 2015
22
0
Thanks!

6. MrChips Moderator

Oct 2, 2009
14,517
4,280
Next question.

How long would it take for the capacitor to charge to the battery voltage?

7. wmodavis Well-Known Member

Oct 23, 2010
739
150
Very long time. Or I should ask how close to the battery voltage do you mean?

8. charmcaster Thread Starter New Member

Jan 13, 2015
22
0
Time constant. For RC circuit its RC.

9. charmcaster Thread Starter New Member

Jan 13, 2015
22
0
capacitor fully charged after five time constants have elapsed.

10. MrChips Moderator

Oct 2, 2009
14,517
4,280
Five time constants is not the correct answer (but is a good answer if you supply an error criteria). See the answer given by wmodavis.

As an exercise, calculate the percent error from fully charged for n time constants (for n = 1 to 10).

What is the error for n = 5 and n= 6?

11. MrAl Distinguished Member

Jun 17, 2014
3,749
791
Hi,

It is interesting how this changed a little over the years. Way back when, 5 time constants was a good enough approximation because it came in very close to the full supply voltage (cap charging through resistor powered by voltage source). But today with the never ending question for resolution and accuracy, that may not be good enough. Back then most measuring instruments could not detect a 0.7 percent difference, or at least it didnt matter that much. These days with high resolution ADC units we probably want 0.5 percent or better, usually better, and with an RC filter somewhere in the input circuit the time we have to wait before we get a good reading (acquisition time) has to be increased.

12. crutschow Expert

Mar 14, 2008
16,551
4,464
I would think the capacitor can be considered effectively fully charged when it is within the capacitor's intrinsic thermal noise level (√kT/C) of the charging voltage.

13. MrChips Moderator

Oct 2, 2009
14,517
4,280
Agreed. When the error is within the noise level we can say it is fully charged.

14. charmcaster Thread Starter New Member

Jan 13, 2015
22
0
Thanks! error for n=5 is 99.3%

15. charmcaster Thread Starter New Member

Jan 13, 2015
22
0
Thank you all!

16. MrChips Moderator

Oct 2, 2009
14,517
4,280
You are very welcome.

Note that the error at n = 5 is 100 - 99.3 = 0.7%

n = 6, error = 0.2%
n = 7, error = 0.1%

charmcaster likes this.

Jan 13, 2015
22
0