1. The problem statement, all variables and given/known data Given a circuit with two resistors, R and r, and a capacitor of C, and EMF of V0 as shown in the diagram, find the voltage across the capacitor during charging. Prove that this voltage, V is given by V = V0 (r/(R+r)) (1-e-((R+r)t)/(RrC)) 2. Relevant equations N.A. 3. The attempt at a solution This is what I have Loop A (with C): V0 + RI + q/c = 0 ==> I = (V0 - VC)/R Loop B (with r): V0 + RI + rIr = 0 I = Ir + Ic ==> I = V/r + C(dv/dt) From first and third, (V0 - VC)/R = V/r + C(dv/dt) Simplify to get, V0 - RC(dv/dt) = V(1+R/r) V = (r/[R+r])(V0 - RC(dV/dt)) The shape of the equation is getting there (I hope), but what do I do next? To get the given equation, RC(dV/dt) must be V0e-((R+r)t)/(RrC). RC (dV/dt) = V, solving this differential equation to get ln (V) = -t/(RC) + k, hence, RC (dV/dt) = e-t/(RC) + k. And I am totally stuck. Did I do something wrong somewhere? I can't think of anyway to get the RrC term in e-((R+r)t)/(RrC), not to mention the V0 and the (R+r) terms, unless k is like Rt/r. But that still does not give me a V0?