In the figure how much charge is stored on the parallel-plate capacitors by the 19.0 V battery? One is filled with air, and the other is filled with a dielectric for which K = 2.70; both capacitors have a plate area of 9.70 x 10-3 m² and a plate separation of 1.50 mm. Number Units eTextbook and Media
In the figure how much charge is stored on the parallel-plate capacitors by the 19.0 V battery? One is filled with air, and the other is filled with a dielectric for which K = 2.70; both capacitors have a plate area of 9.70 x 10-3 m² and a plate separation of 1.50 mm. Number Units eTextbook and Media
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
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![### Problem Statement:
In the figure, how much charge is stored on the parallel-plate capacitors by the 19.0 V battery? One capacitor is filled with air, and the other is filled with a dielectric for which \( \kappa = 2.70 \); both capacitors have a plate area of \( 9.70 \times 10^{-3} \, \text{m}^2 \) and a plate separation of 1.50 mm.
#### Diagram:
The diagram shows two parallel-plate capacitors \( C_1 \) and \( C_2 \) connected in parallel to a battery of voltage \( V \).
\[ V \]
\[ \vert \]
\[ - \text{C_1} \quad \text{C_2} \]
\[ \vert \]
\[ \]
#### Inputs for Calculation:
- **Voltage of battery, \( V \)**: 19.0 V
- **Dielectric constant, \( \kappa \)** for \( C_2 \): 2.70
- **Plate area, \( A \)** for both capacitors: \( 9.70 \times 10^{-3} \, \text{m}^2 \)
- **Plate separation, \( d \)** for both capacitors: 1.50 mm (or \( 1.50 \times 10^{-3} \, \text{m} \))
#### Solution Steps:
1. **Calculate the capacitance for each capacitor:**
For \( C_1 \) (filled with air):
\[
C_1 = \epsilon_0 \frac{A}{d}
\]
where \( \epsilon_0 \) is the permittivity of free space (\( 8.85 \times 10^{-12} \, \text{F/m} \)).
For \( C_2 \) (filled with dielectric \( \kappa = 2.70 \)):
\[
C_2 = \kappa \epsilon_0 \frac{A}{d}
\]
2. **Find the total equivalent capacitance \( C_{\text{eq}} \) for capacitors in parallel:**
\[
C_{\text{eq}} = C_1 + C_2
\]
3. **Calculate the total charge stored using the battery voltage \( V \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba35cc5f-959d-4f80-acdd-e9cc0bd31dfa%2F79485803-8585-4441-86ce-d138d506c193%2F0pxbcc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
In the figure, how much charge is stored on the parallel-plate capacitors by the 19.0 V battery? One capacitor is filled with air, and the other is filled with a dielectric for which \( \kappa = 2.70 \); both capacitors have a plate area of \( 9.70 \times 10^{-3} \, \text{m}^2 \) and a plate separation of 1.50 mm.
#### Diagram:
The diagram shows two parallel-plate capacitors \( C_1 \) and \( C_2 \) connected in parallel to a battery of voltage \( V \).
\[ V \]
\[ \vert \]
\[ - \text{C_1} \quad \text{C_2} \]
\[ \vert \]
\[ \]
#### Inputs for Calculation:
- **Voltage of battery, \( V \)**: 19.0 V
- **Dielectric constant, \( \kappa \)** for \( C_2 \): 2.70
- **Plate area, \( A \)** for both capacitors: \( 9.70 \times 10^{-3} \, \text{m}^2 \)
- **Plate separation, \( d \)** for both capacitors: 1.50 mm (or \( 1.50 \times 10^{-3} \, \text{m} \))
#### Solution Steps:
1. **Calculate the capacitance for each capacitor:**
For \( C_1 \) (filled with air):
\[
C_1 = \epsilon_0 \frac{A}{d}
\]
where \( \epsilon_0 \) is the permittivity of free space (\( 8.85 \times 10^{-12} \, \text{F/m} \)).
For \( C_2 \) (filled with dielectric \( \kappa = 2.70 \)):
\[
C_2 = \kappa \epsilon_0 \frac{A}{d}
\]
2. **Find the total equivalent capacitance \( C_{\text{eq}} \) for capacitors in parallel:**
\[
C_{\text{eq}} = C_1 + C_2
\]
3. **Calculate the total charge stored using the battery voltage \( V \
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