I have a parallel plate capacitor of area A, width d, potential difference V between the plates, and it is disconnected from the source of emf. A wire of resistance R is placed between the plates to allow a current to flow. Draw a sketch to show how the voltage, current and stored energy change over time.
I = (V/R) exp (-t/RC)
The Attempt at a Solution
The capacitance and resistance are constants I think, as they depend only on the physical characteristics of the setup. So I know that I/V will see an exponential decline over time, tending to zero as t tends to infinity. What I don't know, is how each of them varies individually. I presume the potential difference between the plates will tend to zero, so V will decrease over time (exponentially as well?) and that the current can only flow with a voltage difference. I suspect that they both decline exponentially but can't work out how to demonstrate this.
It might involve I = dQ/dt and V= Ed, but I can't get any further than that.
I guess the energy must decline faster though, as U = 0.5CV^2 and V is declining exponentially.
Any help greatly appreciatec