Problem with phase calculation

[tss19]

Here is a question I was given and my solution. I'm not sure where the problem is.

You're given an series RC circuit hooked up to an AC voltage source.
R=5 Ohms, C = 20uF. i(t) = 2cos(5000t) A
Find V(t)

So here's what I did:
Xc = 1/wC = 1/5000*20*10^-6 = 10 Ohm

Z = sqrt(R^2 + Xc^2) = 11.18 Ohm

tan^-1(Xc/R) = phase
tan^-1(10/5) = 63.435 deg.

phasor:
V = IZ = [2/sqrt(2) < 90] * [11.18 < 63.435] = [15.811 < 153.435] V
V(t) = 22.36sin(5000t + 63.435) V

The the problem is with the last line... since this is an RC circuit the current can't possibly be lagging the voltage. The actual result is V(t) = 22.36sin(5000t - 63.435) V

What am I doing wrong?
Thanks!

 

[Laplace]

What you are doing wrong is NOT using what you already know to be true in order to construct the phasor diagram. Recall that for a capacitor with sinusoidal excitation the current leads the voltage by 90 degrees. So the current in this circuit is the same in both the resistor and capacitor. However you may represent the current on the phasor diagram, the resistor voltage will be in-phase with the current and the capacitor voltage will lag the resistor voltage by 90 degrees. Sketch the phasor diagram first, then calculate the exact angle.