What is the voltage across a capacitor after being charged from a 100 V source for a period of one time constant?

 

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.

 

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.

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?

 

Yup.

 

Yup.

Thanks!

 

Next question.

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

 

Very long time. Or I should ask how close to the battery voltage do you mean?

 

Next question.

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

Time constant. For RC circuit its RC.

 

capacitor fully charged after five time constants have elapsed.

 

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?

 

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.

 

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.

 

Agreed. When the error is within the noise level we can say it is fully charged.

 

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?

Thanks! error for n=5 is 99.3%

 

Thank you all!

 

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%

 

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%