How to calculate the initial rate of dischrage of a capacitor.

1. Mar 8, 2010

mike88si

1. The problem statement, all variables and given/known data

A) A DMM with its 10M(ohms symbol) internal resistance is connected to a 9.9 microF capacitor that has been charged to 10 V. Calculate the intial rate of discharge of the capacitor through the DMM in micro-Coulombs per second. Hint: You do not need exponentials for this calculations.

B) Assuming this initial rate of discharge in the question above is maintained for 3 seconds, by what percentage would the capacitor be discharged?

2. Relevant equations

How do I calculate the initial rate of discharge? My lab did not go over it but I Found this formula online but it only goes over time.

T = ( C * V ) / I

3. The attempt at a solution

I = V/R
= (10 / 10
= 1

T = ( C * V ) / I
= (3.9 * 10) / 1
= 39 seconds

So the rate is .1 microF a second?
And if it were discharged for 3 seconds it would be .3 which is 7.6% of the charge discharged.

I am lost! Any help is greatly appreciated, thanks!

2. Mar 8, 2010

Staff: Mentor

You are close when you say I = 10V / 10Meg Ohms (you wrote 10 Ohms, BTW).

After fixing the missing "Meg", you would get I = 1uA

Now you need to convert that into coulombs per second. What is the relationship between Amps and Coulombs per second?

3. Mar 8, 2010

mike88si

The relationship between coulombs per second and amps is that one Amp is one coulomb per second. I think I need this equation:

Q= I * t

t = Q / I also I = Q/t

So to find Q

C = Q/V so we get Q = CV

Q = ( 3.9 * 10^-6 * 10 V ) I = 10/10*10^6
= 3.9*10^-5 couloumbs = 1*10^-6

t = Q / I
= 3.9*10^-5 couloumbs / 1 * 10^-6 couloumbs/second
= 39 seconds

I just realized that what I just did is pretty much the same as above.

4. Mar 9, 2010

Staff: Mentor

Better is $$I = \frac{dQ}{dt}$$

5. Mar 11, 2010

mike88si

thanks. i think i got it. turned it in yesterday.