College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Question:
What is the capacitance of a capacitor with capacitive reactance of 2000 ohm at a frequency of 60 Hz?
### Options:
- 25.6 µF
- 1.33 µF
- 123 µF
- 0.76 µF
### Explanation:
To solve this problem, we can use the formula for capacitive reactance \(X_C\):
\[X_C = \frac{1}{2\pi f C}\]
Where:
- \(X_C\) is the capacitive reactance
- \(f\) is the frequency
- \(C\) is the capacitance
Rearranging the formula to solve for capacitance \(C\):
\[C = \frac{1}{2\pi f X_C}\]
Substitute the given values:
- \(X_C = 2000 \, \text{ohms}\)
- \(f = 60 \, \text{Hz}\)
\[C = \frac{1}{2\pi \times 60 \times 2000}\]
Solve for \(C\) to find the capacitance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c067e04-819e-445d-9345-defba0ea4f93%2Fa7406bd3-5af1-41c7-a6c7-ed3242907daf%2Flfrsf8d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question:
What is the capacitance of a capacitor with capacitive reactance of 2000 ohm at a frequency of 60 Hz?
### Options:
- 25.6 µF
- 1.33 µF
- 123 µF
- 0.76 µF
### Explanation:
To solve this problem, we can use the formula for capacitive reactance \(X_C\):
\[X_C = \frac{1}{2\pi f C}\]
Where:
- \(X_C\) is the capacitive reactance
- \(f\) is the frequency
- \(C\) is the capacitance
Rearranging the formula to solve for capacitance \(C\):
\[C = \frac{1}{2\pi f X_C}\]
Substitute the given values:
- \(X_C = 2000 \, \text{ohms}\)
- \(f = 60 \, \text{Hz}\)
\[C = \frac{1}{2\pi \times 60 \times 2000}\]
Solve for \(C\) to find the capacitance.
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