Obtain Expression For Voltage Across Capacitor

  • #1

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
 

Answers and Replies

  • #2
gneill
Mentor
20,913
2,862
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.
 
  • #3
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
 

Related Threads on Obtain Expression For Voltage Across Capacitor

Replies
7
Views
22K
Replies
1
Views
930
Replies
6
Views
1K
  • Last Post
Replies
5
Views
2K
Replies
11
Views
1K
Replies
3
Views
1K
Top