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## 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.

Answer known to be: ##v_c(t)=15.57cos(2\pi\times10^3t-81.5^\circ)##

## Homework Equations

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