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Obtain Expression For Voltage Across Capacitor
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[QUOTE="Captain1024, post: 4950075, member: 507487"] [h2]Homework Statement [/h2] 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)## [h2]Homework Equations[/h2] V = IR [h2]The Attempt at a Solution[/h2] By KVL: ##25\angle-30^\circ=RI+\frac{1}{j\omega C}I## ##\Rightarrow\ 25\angle-30^\circ=I(R-\frac{j}{\omega C})## [SIZE=6]##\Rightarrow\ I=\frac{25\angle-30^\circ}{R-\frac{j}{\omega C}}##[/SIZE] 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 [/QUOTE]
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Obtain Expression For Voltage Across Capacitor
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