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## Homework Statement

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.

## Homework Equations

I=C(dv/dt) Through capacitor

I=V/R Through Resistance.

## 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?