RC Circuit: Phase & Magnitude of Current

[tjr39]

Homework Statement

Given an RC circuit which has a Capacitor$(C=6\times 10^{-6} F)$ and a resistor $(R=5 \Omega)$conected in series to an a.c. voltage source of the form $v=V_{0} e^{j\omega t}$with a $V_{0}$=1 Volt. Frequency f=10kHz
a)What is the phase of the current with respect to the applied voltage?
b) What is the magnitude of the current?

Homework Equations

$Z=Z_{R}+Z_{C}$

$Z_{C}$=$\frac{1}{j\omega C}$

Z=x+jy where j=$\sqrt{-1}$

Z=ze$^{j \phi}$ with z=$\sqrt{x^{2}+y^{2}}$ and $\phi =tan^{-1}$$\frac{y}{x}$

$\omega = 2\pi \times f$

The Attempt at a Solution

$\frac{1}{\omega C} = 2.65$

Z=R+ $\frac{1}{j\omega C}$

=5-2.65j

Which can be written as $Z=ze^{j\phi}$

$z=\sqrt{5^{2}+2.65^{2}}=5.66$

$\phi =tan^{-1}\frac{-2.65}{5}=-27.9 degrees$

Since $i=\frac{V_{0}}{z}e^{j(\omega t-\phi)}$ then I can say the current leads the voltage by 27.9 degrees.

And I can also say the magnitude of the current i is equal to $\frac{V_{0}}{z}=\frac{1}{5.66}$

How did I go?? Am I on track anywhere at all or have I made a bit of a mess of it?

 

[gneill]

The calculations look fine. The results are good.

 

[CrazyNinja]

Everything look allright.