Wrong value for the voltage across a capacitor

Click For Summary
SUMMARY

The discussion centers on calculating the voltage across a 100 microfarad capacitor given the current function i(t) = 50 sin(120πt) mA. The correct voltage at t = 1 ms is 93.14 mV, as stated in the reference book. The user initially calculated v(t) as -2.87 x 10^(-5) V due to an error in using degrees instead of radians for the cosine function. The final resolution confirmed that the negative sign in the voltage equation must be addressed to yield a positive result.

PREREQUISITES
  • Understanding of capacitor voltage-current relationships
  • Familiarity with integral calculus
  • Knowledge of trigonometric functions in radians
  • Basic electrical engineering concepts
NEXT STEPS
  • Review capacitor charging equations in electrical circuits
  • Study the application of integral calculus in electrical engineering
  • Learn about the importance of radians in trigonometric calculations
  • Explore common mistakes in voltage calculations across capacitors
USEFUL FOR

Students in electrical engineering, physics students tackling circuit analysis, and anyone interested in understanding capacitor behavior in AC circuits.

AfterSunShine
Messages
27
Reaction score
3

Homework Statement


The current through a 100 microfarad is i(t) = 50 sin(120*pi*t) mA
Calculate the voltage across it at t = 1 ms. Consider zero initial voltage.

Homework Equations


v(t) = (1/c) integral of i(t) from t = 0 to t = t

The Attempt at a Solution


Am getting v(t) = - 1.326 ( cos(120*pi*t) - 1 ) V
which gives v(1*10^-3) = -2.87 * 10^(-5) V
But book is saying the voltage should be 93.14 mV

Can any confirm if book answer is correct?
I did the problem like 100 times, and still same value. I considered that given current in mA so I multiplied by 10^-3, and considered the 10^-6 from micro farad. integral of sin(120*p*t) is -cos(120*pi*t) / (120*pi)
I have no idea where is my mistake.
 
Physics news on Phys.org
The book's answer is correct, but so is most of your calculations. When you computed ## \cos(.377) ## , did you use radians or degrees? You need to use radians. ## \\ ##Edit: And yes, I tried the arithmetic with degrees, and I got very close to your (incorrect) answer, but I get +2.87 E-5, with a "+" sign.
 
Last edited:
  • Like
Likes AfterSunShine
So i substitute pi with 180.
And yes you are correct, while calculating final answer i forget to include the "-" sign
I have negative sign in my v(t), and there will (cos(something) - 1) which will give minus for sure as maximum value for cosine is 1, with the negative in v(t), answer must be positive
Thanks!
 
  • Like
Likes Charles Link

Similar threads

Replies
0
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 17 ·
Replies
17
Views
2K
  • · Replies 9 ·
Replies
9
Views
7K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
2
Views
3K
  • · Replies 21 ·
Replies
21
Views
4K
Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K