Derive the Voltage and Current equations for Step Response of an RC circuit.
End products will be Vc(t) = i(s)R + (Vo - i(s)R)e^(-t/RC) and i(t) = (Is - (Vo/R))e^(-t/RC)
The Attempt at a Solution
Using KCL on a hypotetical RC circuit with a current source in parallel with a resistor, which is parallel to a capacitor, I end up with i(R)+i(c)=i(s) which converts to (V(c)/R) + C(dv/dt) = i(s). After rearranging I get (V(c)/RC) + (d(v)/d(t)) = (i(s)/C) then (d(v)/d(t)) = (i(s)/C) - (V(c)/RC). I am now stumped as to how to procede. Anybody have any ideas? Thanks!