### Capacitor Capacitance Comparison ExerciseThe plate areas and plate separations of five parallel plate capacitors are defined as follows:**Capacitor Specifications:**1. **Capacitor 1:** Area \( A \), Separation \( d \)2. **Capacitor 2:** Area \( 2A \), Separation \( 2d \)3. **Capacitor 3:** Area \( 2A \), Separation \( \frac{d}{2} \)4. **Capacitor 4:** Area \( \frac{A}{2} \), Separation \( 2d \)5. **Capacitor 5:** Area \( A \), Separation \( \frac{d}{2} \)**Task:**Rank these capacitors according to their capacitances from **Least to Greatest**. Options for ranking the capacitances:1. 4, 1 and 2 tie, 5, 32. 1, 2, 3, 4, 53. 5, 4, 3, 2, 14. 4, 1 and 2 tie, 5, 35. 3, 5, 1 and 2 tie, 4### Explanation:1. **Capacitance Formula for a Parallel Plate Capacitor** The capacitance \( C \) of a parallel plate capacitor is given by the formula: \[ C = \frac{\epsilon_0 A}{d} \] where \( \epsilon_0 \) is the permittivity of free space, \( A \) is the area of one plate, and \( d \) is the separation between the plates.2. **Applying the Formula to Given Capacitors:** - **Capacitor 1:** \( \frac{\epsilon_0 A}{d} \) - **Capacitor 2:** \( \frac{\epsilon_0 2A}{2d} = \frac{\epsilon_0 A}{d} \) - **Capacitor 3:** \( \frac{\epsilon_0 2A}{d/2} = \frac{4\epsilon_0 A}{d} \) - **Capacitor 4:** \( \frac{\epsilon_0 (A/2)}{2d

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capacitances from Least to Greatest

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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### Capacitor Capacitance Comparison Exercise

The plate areas and plate separations of five parallel plate capacitors are defined as follows:

**Capacitor Specifications:**
1. **Capacitor 1:** Area \( A \), Separation \( d \)
2. **Capacitor 2:** Area \( 2A \), Separation \( 2d \)
3. **Capacitor 3:** Area \( 2A \), Separation \( \frac{d}{2} \)
4. **Capacitor 4:** Area \( \frac{A}{2} \), Separation \( 2d \)
5. **Capacitor 5:** Area \( A \), Separation \( \frac{d}{2} \)

**Task:**
Rank these capacitors according to their capacitances from **Least to Greatest**.

Options for ranking the capacitances:
1. 4, 1 and 2 tie, 5, 3
2. 1, 2, 3, 4, 5
3. 5, 4, 3, 2, 1
4. 4, 1 and 2 tie, 5, 3
5. 3, 5, 1 and 2 tie, 4

### Explanation:

1. **Capacitance Formula for a Parallel Plate Capacitor**
The capacitance \( C \) of a parallel plate capacitor is given by the formula:
\[
C = \frac{\epsilon_0 A}{d}
\]
where \( \epsilon_0 \) is the permittivity of free space, \( A \) is the area of one plate, and \( d \) is the separation between the plates.

2. **Applying the Formula to Given Capacitors:**
- **Capacitor 1:** \( \frac{\epsilon_0 A}{d} \)
- **Capacitor 2:** \( \frac{\epsilon_0 2A}{2d} = \frac{\epsilon_0 A}{d} \)
- **Capacitor 3:** \( \frac{\epsilon_0 2A}{d/2} = \frac{4\epsilon_0 A}{d} \)
- **Capacitor 4:** \( \frac{\epsilon_0 (A/2)}{2d

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