RC Circuit with alternating voltage source

[sun18]

Homework Statement

I'm supposed to find the current in a circuit with a voltage source, capacitor, and resistor in series. The voltage source is described by V=V₀e^jwt.
Here, j is the complex number j²=-1, and i is the current

Homework Equations

I=C*dv/dt

The Attempt at a Solution

I have several sources of confusion with this question. First, in the equation I=C*dv/dt, does that v refer to the voltage source, or specifically the voltage drop across the capacitor? Can I use Kirchoff's voltage law with this type of circuit? I tried this and got:

V₀e^jwt - iR - q/c = 0
Then taking the time derivative of the equation:

V₀jwe^jwt - R*di/dt - i/c = 0
I then have no idea how to solve this differential equation. Even rewriting with euler's identity:
V₀jw[cos(wt)+jsin(wt)]=R*di/dt+i/c

Any help would be greatly appreciated.

 

[gneill]

I suspect that the ##V = V_o e^{j \omega t}## is meant to be a phasor representation for the input. Have you covered phasors yet? If so you're meant to deal with the real portion of the resulting voltage, which in this case would be ##V_o cos(\omega t)##.

Yes, the v in I = C*dv/dt represents the voltage across the capacitor.

Yes, Kirchhoff's Voltage Law (KVL) can be applied as you have done.

 

[sun18]

We haven't covered phasors yet but I read ahead and it makes sense now.
Thank you for the response.