plates of a capacitor are 4.0 mm apart i. C/m?. Calculate the energy density in betwe 5. A capacitor circuit is shown in figure. Calculate the equivalent capacitance of the circuit. b. Calculate the charge on capacitor C1. a. C2= 2 mF 5.0 V C4= 3 mF ic field C1= 1mF C3=2 mF
plates of a capacitor are 4.0 mm apart i. C/m?. Calculate the energy density in betwe 5. A capacitor circuit is shown in figure. Calculate the equivalent capacitance of the circuit. b. Calculate the charge on capacitor C1. a. C2= 2 mF 5.0 V C4= 3 mF ic field C1= 1mF C3=2 mF
College Physics
11th Edition
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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![**Educational Content on Capacitor Circuits**
**Question 5:**
- The parallel plates of a capacitor are **4.0 mm** apart in a medium with a permittivity of **\(5.6 \times 10^{-11} F/m\)**. Calculate the energy density between the plates.
**Question 6:**
A capacitor circuit is shown in the figure.
a. Calculate the equivalent capacitance of the circuit.
b. Calculate the charge on capacitor \(C_1\).
**Diagram Explanation:**
The diagram shows a circuit with a voltage source of **5.0 V** connected to a combination of capacitors:
- \(C_1 = 1 \, \text{mF}\)
- \(C_2 = 2 \, \text{mF}\)
- \(C_3 = 2 \, \text{mF}\)
- \(C_4 = 3 \, \text{mF}\)
Capacitors \(C_2\) and \(C_3\) are connected in parallel. The combination of \(C_2\) and \(C_3\) is in series with \(C_4\). This entire arrangement is connected in parallel with \(C_1\).
To solve this:
1. Calculate the equivalent capacitance of \(C_2\) and \(C_3\) which are in parallel:
\[
C_{23} = C_2 + C_3
\]
2. Calculate the equivalent capacitance of \(C_{23}\) in series with \(C_4\):
\[
C_{234} = \left( \frac{1}{C_{23}} + \frac{1}{C_4} \right)^{-1}
\]
3. Finally, add \(C_{234}\) in parallel with \(C_1\) to find the total equivalent capacitance \(C_{\text{eq}}\):
\[
C_{\text{eq}} = C_{234} + C_1
\]
For the charge on \(C_1\), use:
\[
Q_1 = C_1 \times \text{Voltage across } C_1
\]
The voltage across \(C_1\) is the same as the source voltage since they are in parallel.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6a5d441-691e-4a20-a4ea-52e6f9df3d14%2Fbfb1d944-0655-40b1-b0c3-beba10b380cb%2Fslagm6b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content on Capacitor Circuits**
**Question 5:**
- The parallel plates of a capacitor are **4.0 mm** apart in a medium with a permittivity of **\(5.6 \times 10^{-11} F/m\)**. Calculate the energy density between the plates.
**Question 6:**
A capacitor circuit is shown in the figure.
a. Calculate the equivalent capacitance of the circuit.
b. Calculate the charge on capacitor \(C_1\).
**Diagram Explanation:**
The diagram shows a circuit with a voltage source of **5.0 V** connected to a combination of capacitors:
- \(C_1 = 1 \, \text{mF}\)
- \(C_2 = 2 \, \text{mF}\)
- \(C_3 = 2 \, \text{mF}\)
- \(C_4 = 3 \, \text{mF}\)
Capacitors \(C_2\) and \(C_3\) are connected in parallel. The combination of \(C_2\) and \(C_3\) is in series with \(C_4\). This entire arrangement is connected in parallel with \(C_1\).
To solve this:
1. Calculate the equivalent capacitance of \(C_2\) and \(C_3\) which are in parallel:
\[
C_{23} = C_2 + C_3
\]
2. Calculate the equivalent capacitance of \(C_{23}\) in series with \(C_4\):
\[
C_{234} = \left( \frac{1}{C_{23}} + \frac{1}{C_4} \right)^{-1}
\]
3. Finally, add \(C_{234}\) in parallel with \(C_1\) to find the total equivalent capacitance \(C_{\text{eq}}\):
\[
C_{\text{eq}} = C_{234} + C_1
\]
For the charge on \(C_1\), use:
\[
Q_1 = C_1 \times \text{Voltage across } C_1
\]
The voltage across \(C_1\) is the same as the source voltage since they are in parallel.
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