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## Homework Statement

I am given an RC circuit with an alternating current. The circuit contains a capacitor and a resistor in parallel. Part (a) says "Use KCL to find a differential equation for I in terms of V." Part (b) says "For an applied voltage V = V

_{o}exp(iwt), find the current I."

## Homework Equations

I

_{Total}= I

_{1}+ I

_{2}

Z = impedance

Z

_{R}= R

Z

_{C}= (1/wiC)

V = IZ

## The Attempt at a Solution

I understand how KCL works, but I'm not sure how to get it in a differential equation. Ignoring this and using KCL anyway, I get:

V - I

_{1}Z

_{R}= V - I

_{1}R = 0

V - I

_{2}Z

_{C}= V - I

_{2}(1/iwC) = 0

I

_{1}= ViwC

I

_{2}= (V/R)

I

_{Total}= ViwC + (V/R)

Am I on the right track, or does the fact that I need a differential equation mean I need to do something completely different?

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