- #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 R0
Homework Equations
(1) I = (Q0/RC)e-t/RC
(2,3) Q0=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=R0, I tried to use equation (1) for R and at t = 0, when R = R0, so that I could equate the two equations and try to solve for R. This is what I started with:
Q0/R0C0 = (Q/RC)e-t/RC
I ended up with something like:
R = (QR0C0/Q0C)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?