Question

Why capacitor charge and discharge exponentially why it does not charge and discharge linearly?

Answer 1

it is not a linear device ,,it has storing capability thats the reason why it charges and discharges exponentially.

Answer 2

Because with a constant voltage source you are trying to force electrons onto a metal plate. The more electrons you have on the plate, the harder it gets to put more on it (because a voltage opposite to the power source is slowly building.) Discharging is the same. At first there is a great amount of voltage across the plates. The electrons on one side are leaving through the leads on the cap because they are attracted to the positive charge on the other side, which is connected through the circuit. But as the amount of charge depleats, so does the attractive force. This is one of many cases in nature where the time rate of change of a quantity depends on how much of that quantity is left. This is the same phenomenon in nuclear decay. These kinds of functions will always include the exponential function, due to the integral of 1/x dx. which is what you'll get to if you set up the equation -dx/dt = kx. This becomes -1/x dx = k dt. integrate both sides to get -ln(x) = kt. Raise both sides as exponents of e to get rid of logarithm and put the negative sign on the other side to get x = e^-(kt).

Answer 3

I should have pointed out that the equation I set up -dx/dt = kx is what I said in words. The rate of decay in time of a quantity x (-dx/dt) is proportional to (constant k) the amount left: x.