College Physics
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ISBN: 9781305952300
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![### Capacitor Arrangement and Potential Difference
In the figure, a potential difference \( V = 98.0 \, \text{V} \) is applied across a capacitor arrangement with the following capacitances:
- \( C_1 = 14.6 \, \mu\text{F} \)
- \( C_2 = 5.34 \, \mu\text{F} \)
- \( C_3 = 3.02 \, \mu\text{F} \)
We aim to find the following:
1. The charge \( q_3 \) on capacitor 3.
2. The potential difference \( V_3 \) across capacitor 3.
3. The stored energy \( U_3 \) in capacitor 3.
4. The charge \( q_1 \) on capacitor 1.
5. The potential difference \( V_1 \) across capacitor 1.
6. The stored energy \( U_1 \) in capacitor 1.
7. The charge \( q_2 \) on capacitor 2.
8. The potential difference \( V_2 \) across capacitor 2.
9. The stored energy \( U_2 \) in capacitor 2.
#### Diagram Explanation
The diagram shows a combination of capacitors where capacitors \( C_1 \) and \( C_2 \) are in series with each other, while their combination is in parallel with capacitor \( C_3 \). The potential difference across the entire arrangement is \( V = 98.0 \, \text{V} \).
1. **Calculate the Equivalent Capacitance:**
- **Series combination of \( C_1 \) and \( C_2 \):**
\[
\frac{1}{C_{1,2}} = \frac{1}{C_1} + \frac{1}{C_2}
\]
\[
C_{1,2} = \frac{1}{\left(\frac{1}{14.6 \, \mu\text{F}} + \frac{1}{5.34 \, \mu\text{F}}\right)}
\]
- **Total equivalent capacitance \( C_{eq} \):**
\[
C_{eq} = C_{1,2} + C_3
\]
2. **Calculate the charge stored on](https://content.bartleby.com/qna-images/question/af1ef7c6-a145-4dbc-a50b-84dc7d2e578d/73a3396e-ee36-42ed-97eb-c0e20d7447b8/gbhl3fe_processed.jpeg)
Transcribed Image Text:### Capacitor Arrangement and Potential Difference
In the figure, a potential difference \( V = 98.0 \, \text{V} \) is applied across a capacitor arrangement with the following capacitances:
- \( C_1 = 14.6 \, \mu\text{F} \)
- \( C_2 = 5.34 \, \mu\text{F} \)
- \( C_3 = 3.02 \, \mu\text{F} \)
We aim to find the following:
1. The charge \( q_3 \) on capacitor 3.
2. The potential difference \( V_3 \) across capacitor 3.
3. The stored energy \( U_3 \) in capacitor 3.
4. The charge \( q_1 \) on capacitor 1.
5. The potential difference \( V_1 \) across capacitor 1.
6. The stored energy \( U_1 \) in capacitor 1.
7. The charge \( q_2 \) on capacitor 2.
8. The potential difference \( V_2 \) across capacitor 2.
9. The stored energy \( U_2 \) in capacitor 2.
#### Diagram Explanation
The diagram shows a combination of capacitors where capacitors \( C_1 \) and \( C_2 \) are in series with each other, while their combination is in parallel with capacitor \( C_3 \). The potential difference across the entire arrangement is \( V = 98.0 \, \text{V} \).
1. **Calculate the Equivalent Capacitance:**
- **Series combination of \( C_1 \) and \( C_2 \):**
\[
\frac{1}{C_{1,2}} = \frac{1}{C_1} + \frac{1}{C_2}
\]
\[
C_{1,2} = \frac{1}{\left(\frac{1}{14.6 \, \mu\text{F}} + \frac{1}{5.34 \, \mu\text{F}}\right)}
\]
- **Total equivalent capacitance \( C_{eq} \):**
\[
C_{eq} = C_{1,2} + C_3
\]
2. **Calculate the charge stored on
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