Answer to Question #112561 in Calculus for Simon

Question

A discharging circuit has a voltage across the capacitor of v = V e^((-t)/RC) Determine dv/dt, the rate of change in voltage in the discharging circuit capacitor. Then find dv/dt when t = T.

Answer 1

Given $v = V e^{-t/RC}$ .

So, $\frac{dv}{dt} = V \frac{-1}{RC} e^{-t/RC} =-\frac{V}{RC} e^{-t/RC}$ .

Now $dv/dt$ at t=T is $\frac{dv}{dt}|_{t=T} =-\frac{V}{RC} e^{-T/RC}$