# Finding the time constant in a RC circuit given no time?

Discussion in 'Homework Help' started by ABCJ6, Dec 4, 2014.

1. ### ABCJ6 Thread Starter New Member

Dec 4, 2014
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0
I'm a little unsure of how to go about with this question for part b since i wasn't given a time for it.

An 18 μF capacitor has been charged to 100V. A15 kΩ resistor

and a 5 kΩ resistor, are connected in series with the capacitor.

(a) What is the time constant of this circuit? (found this to be 0.36s)
(b) Approximately how long (in terms of τ) will it take for the
charge stored on the resistor to drop to 0.1% of its original
charge?

2. ### Papabravo Expert

Feb 24, 2006
11,123
2,171
An RC circuit is described by a first order differential equation. You solve that differential equation. Form the solution, you plug in the time constant and the final value and solve for t, the time it takes to reach the final value. Can you do that?

3. ### ABCJ6 Thread Starter New Member

Dec 4, 2014
2
0
okay, thank you!!

4. ### WBahn Moderator

Mar 31, 2012
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5,747
Since there isn't any charge stored on the resistor, it won't take any time for it to drop to 0.1% of that.

Now, if you were asked how many time constants does it take for a quantity to exponentially decay to 0.1% of it's initial value, that will have the same answer regardless of what the time constant is or whether we are talking about charge on a capacitor, current in an inductor, amount of radioactive material, whatever.

5. ### MrAl Distinguished Member

Jun 17, 2014
3,721
789

Hi,

Are you sure you wrote part (b) the way it was supposed to be written? There is no charge 'stored' on the resistor, the charge is stored in the capacitor.

Also, i dont think you should have to resort to differential equations for this simple circuit unless you have never done this before. The well known solutions are:

Vc=Vs*(1-e^(-t/RC))
and
Vc=Vc(0)*e^(-t/RC)

Vs is source voltage, Vc(0) is initial cap voltage.
You'll have to figure out which one to use for a given problem.

6. ### Papabravo Expert

Feb 24, 2006
11,123
2,171
Charge on a resistor. I missed that minor detail. Good catch.