1. The problem statement, all variables and given/known data A 68 nF capacitor has a parasitic parallel resistance Rp = 1 MΩ. If a voltage V = Vmsin(ωt) is applied, as shown in the diagram, find the frequencies at which: 1. The current amplitude through the parasitic resistance is 1% of the current amplitude through the capacitor. 2. The amplitudes of the currents through the resistor and the capacitor are equal. 2. Relevant equations I=C(dv/dt) Through capacitor I=V/R Through Resistance. 3. The attempt at a solution I want to try to solve the second part of the question first because it would provide be a more fundamental solution. In any case, I've equated the current through the capacitor with the current through the parasitic resistor: Cdv/dt = V/Rp Simple enough. Now V=Vmsin(wt) so dv/dt = (w)(Vm)(Cos)(wt) Substituting in we get: (C)(w)(Vm)(Cos)(wt) = Vmsin(wt)/(Rp). so: (Rp)(C)(w)(Vm)(Cos)(wt) = Vmsin(wt) <-- just moving the resistance to the other side At t=0. We know that sin waves have 0 amplitude, and cos waves have 1 amplitude. So setting t=0. (Rp)(C)(w) = 0 Or in another words w=0, and frequency also =0. Clearly that isn't correct though. What am I missing. --------------------------------------- At the stage Cdv/dt = V/Rp I've tried integrating both sides with respect to dv and dt. which produces: (C)(Rp)V = -(1/W)(V)(Cos(wt)) When t=0. -(C)(Rp)(W) = 1 And we can solve for W and thus frequency. that produces the right answer, but I can't see why the first approach produces the answer f=0. I think the problem is to do with how I've used/understood calculus in the first attempt. Can anyone shed any light?