This is a review question that could be on my Calc 2 test.
The circuit equation is
R dQ/dt + Q/C = E
or after dividing by R,
dQ/dt + Q/(RC) = E/R
subject to the initial condition
Q(0) = 0 (assuming the capacitor is uncharged at t=0)
This is a simple first-order linear equation which you should have no trouble solving. The solution is
Q = CE( 1 - e^(-t/(RC))
The current i is dQ/dt:
i = (E/R)(e^(-t/RC))
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Verified answer
The circuit equation is
R dQ/dt + Q/C = E
or after dividing by R,
dQ/dt + Q/(RC) = E/R
subject to the initial condition
Q(0) = 0 (assuming the capacitor is uncharged at t=0)
This is a simple first-order linear equation which you should have no trouble solving. The solution is
Q = CE( 1 - e^(-t/(RC))
The current i is dQ/dt:
i = (E/R)(e^(-t/RC))