Physics 2
posted by Robert .
Show that during the charging of the capacitor in an RC circuit, the charge of the capacitor, as a function of time, is: q(t) = C(1 – et/RC)

the character that doesn't show up is the emf (E)

The current is
i = dq/dt = C*E*(1/RC)*e^(t/RC)
= (E/R)*e^(t/RC)
iR + q/C = E*e^(t/RC)+ E*(1 – e^t/RC)
= E
Therefore the sum of the voltage drop across the capacitor and the resistor equals E at all times, as required. 
thank you very much drwls, this is a question from a sample exam, getting ready for my finals tomorrow!

Good luck with finals! I took a lazy approach to your question, showing that what you wrote is the solution, rather than solving the general differential equation.

thanks. It's all good, I understand your approach and I really appreciate it!