- #1

ddobre

- 33

- 2

## Homework Statement

A charged capacitor with capacitance C is being discharged through a variable resistor that has its resistance dependent on time: R = R(t). Find function R(t) if the current through the resistor remains constant until the capacitor is completely discharged and the resistance at the initial moment of the discharge process (t = 0) is equal to R

_{0}

## Homework Equations

(1) I = (Q

_{0}/RC)e

^{-t/RC}

(2,3) Q

_{0}=Cε, Q = Cεe

^{-t/RC}

t = RC

IR = Q/C

## The Attempt at a Solution

Since I know I is contant, and at t = 0, R=R

_{0}, I tried to use equation (1) for R and at t = 0, when R = R

_{0}, so that I could equate the two equations and try to solve for R. This is what I started with:

Q

_{0}/R

_{0}C

_{0}= (Q/RC)e

^{-t/RC}

I ended up with something like:

R = (QR

_{0}C

_{0}/Q

_{0}C)e

^{-t/RC}

But I was a little confused because there is still an R in the e expression. So I tried taking the natural log of each side, but what I ended up with didn't seem feasible. Any advice on what I should try to do?