Wrong value for the voltage across a capacitor

In summary, the conversation involves calculating the voltage across a 100 microfarad capacitor at t = 1 ms, given the current i(t) = 50 sin(120*pi*t) mA and zero initial voltage. The textbook answer is 93.14 mV, while the OP's calculations result in -2.87 * 10^(-5) V. The discrepancy is due to the use of degrees instead of radians in the computation of cos(120*pi*t). After correcting this mistake, the answer matches with the textbook.
  • #1
AfterSunShine
27
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
  • #2
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
  • #3
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

1. How do I know if the voltage across a capacitor is wrong?

The voltage across a capacitor can be measured using a voltmeter. If the measured voltage does not match the expected value, then it is considered to be wrong.

2. What could cause the voltage across a capacitor to be wrong?

There are a few possible causes for a wrong voltage across a capacitor, including faulty components, incorrect connections, or an incorrect calculation of the expected voltage.

3. How can I fix a wrong voltage across a capacitor?

If the voltage is wrong due to a faulty component or connection, it can be fixed by replacing the faulty part or correcting the connection. If the incorrect voltage is due to a calculation error, double-check the formula used to calculate the voltage and make any necessary corrections.

4. Can a wrong voltage across a capacitor cause damage?

In most cases, a wrong voltage across a capacitor will not cause any damage. However, if the voltage is too high, it can lead to overheating and possibly damage the capacitor. It is important to ensure that the correct voltage is applied to a capacitor to prevent any potential damage.

5. What is the correct way to measure the voltage across a capacitor?

The voltage across a capacitor should be measured using a voltmeter connected in parallel with the capacitor. This will give an accurate reading of the voltage across the component. It is important to ensure that the voltmeter is set to the correct range for the expected voltage.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
0
Views
513
  • Engineering and Comp Sci Homework Help
Replies
17
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
7
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
9
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
10
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
8
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
21
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
9
Views
6K
Back
Top