RC Circuit with a voltage source

[RyanP]

Homework Statement

A voltage source E_0 cos ωt is connected in series with a resistor R and a capacitor C. Write down the differential equation expressing Kirchhoff’s law. Then guess an exponential form for the current, and take the real part of your solution to find the actual current. Determine how the amplitude and phase of the current behave for very large and very small ω, and explain the results physically.

Homework Equations

The Attempt at a Solution

[/B]
I got the complex current to be I(t) = [(iωE0/R)/(1/RC + iω)] * e^(iωt)

I just don't know how to convert this back to real current. I know e^(iωt) = cos(ωt)+isin(ωt), but how do I deal with the rest of the term?

 

[haruspex]

I know e^(iωt) = cos(ωt)+isin(ωt), but how do I deal with the rest of the term?

Plug that in and multiply out.

 

[ehild]

Homework Statement

A voltage source E_0 cos ωt is connected in series with a resistor R and a capacitor C. Write down the differential equation expressing Kirchhoff’s law. Then guess an exponential form for the current, and take the real part of your solution to find the actual current. Determine how the amplitude and phase of the current behave for very large and very small ω, and explain the results physically.

Homework Equations

The Attempt at a Solution

[/B]
I got the complex current to be I(t) = [(iωE0/R)/(1/RC + iω)] * e^(iωt)

I just don't know how to convert this back to real current. I know e^(iωt) = cos(ωt)+isin(ωt), but how do I deal with the rest of the term?

You have the current as the product I=G E₀e^iωt. G=|G|e^iφ. Find the magnitude |G| and the phase φ, then I=|G|E₀e^i(ωt+φ). Take the real part.