Calculating Current Split in Parallel Circuit with Frequency of 100 sec-1

[awakeinroom8]

Homework Statement

A capacitor is placed parallel across a resistive load in a circuit. C= 0.829*10-6 F and R = 229 ohms. What fraction of the current goes through the capacitor when the frequency is 100 sec-1?

Homework Equations

I(resistor) = V/R
I(capacitor) = C * (dV/dt) = ω*C*V (?)

The Attempt at a Solution

Ic / (Ir + Ic) = [ω*C*V] / [(V/R) + (ω*C*V)] reduces to [ω*C*R] / [1 + ω*C*R]
The answer I got was 0.106569. I don't know if the work is wrong or if the format of my answer wrong, like is that the "fraction" or do I have to do something else to it? Thanks.

 

[ideasrule]

The problem here is that I_tot does not equal Ir+Ic. The instantaneous current at any point in time does obey I_tot=Ir+Ic, but not the effective current in an AC circuit. You have to calculate the total effective current in a different way (what way?)

 

[awakeinroom8]

The only thing I can find is for an RC circuit in series. is it the same for parallel?

 

[awakeinroom8]

do you mean I_tot (sqrt 2)? can someone please help me it's almost due :/