Peoples Physics Concepts

http://www.ck12.org Chapter 15. Electric Circuits: Capacitors

Q(t) =Qoe

−τt

start with the equation give above

. 1 Qo=Qoe
−τt
substitute. 1 QoforQ(t)because that’s the charge at the time we want to find
. 1 =e

−τt

simplify the equation

t=−τln(. 1 ) solve for time

t=−RCln(. 1 ) substitute in the value forτ

t=− 100 Ω∗ 500 μF∗ln(. 1 ) substitute in all the known values

t=.12 s

(b): Solving the second part of this problem will be a two step process. We will use the capacitance and the voltage

drop to determine how much charge was originally on the capacitor (Qo).

Qo=CV

Qo= 500 μF∗12 V

Qo=.006 C

Now we can plug in the time we found in part A to the equation for charge as a function of time.

Q(t) =Qoe

−τt

Q(.12 s) =.006 Ce

100 −Ω.∗12 s 500 μF

Q(.12 s) = 5. 44 ∗ 10 −^4 C

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1. Design a circuit that would allow you to determine the capacitance of an unknown capacitor.