(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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."

2. Relevant equations

I_{Total}= I_{1}+ I_{2}

Z = impedance

Z_{R}= R

Z_{C}= (1/wiC)

V = IZ

3. 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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# Homework Help: RC circuit with AC - finding current

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