# Obtain Expression For Voltage Across Capacitor

## Homework Statement

A voltage source given by ##v_s(t)=25cos(2\pi\times10^3t-30^\circ)## is connected to a series RC load. If R = 1MOhm and C = 200pF, obtain an expression for ##v_c(t)##, the voltage across the capacitor.

V = IR

## The Attempt at a Solution

By KVL: ##25\angle-30^\circ=RI+\frac{1}{j\omega C}I##

##\Rightarrow\ 25\angle-30^\circ=I(R-\frac{j}{\omega C})##

##\Rightarrow\ I=\frac{25\angle-30^\circ}{R-\frac{j}{\omega C}}##

Plugging in values: ##I=1.95\times10^{-5}\angle-68.52^\circ##

Now, my thinking was that Ohm's law works for phasor impedances: ##V_c=IZ##, where ##Z=\frac{1}{j\omega C}##. However, that yielded an answer with the same magnitude as the current I found above. What am I missing?

Thanks
-Captain1024

gneill
Mentor
Your current magnitude looks about right, but the phase angle looks off to me. Check your math on that.

Ohm's law does indeed work for phasor values.

I redid the math. The angle of the current should be positive 8.52 deg. Then, earlier I made the mistake of trusting my calculator to convert rec to polar. I did it by hand with the correct current and got the right answer. Thanks for the guidance.

-Captain1024