4. Using the given circuit, where V = 6V, C₁ = 470 µF, C2 = 330 μF, and C3 = 100μF, determine charges and energies stored on each capacitor. C₁ C3 -C₂ 45
4. Using the given circuit, where V = 6V, C₁ = 470 µF, C2 = 330 μF, and C3 = 100μF, determine charges and energies stored on each capacitor. C₁ C3 -C₂ 45
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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![**Problem 4: Capacitor Circuit Analysis**
**Objective:**
Using the given circuit, where \( V = 6 \text{V} \), \( C_1 = 470 \,\mu\text{F} \), \( C_2 = 330 \,\mu\text{F} \), and \( C_3 = 100 \,\mu\text{F} \), determine the charges and energies stored on each capacitor.
**Description of the Circuit Diagram:**
The diagram depicts a circuit with three capacitors. Capacitor \( C_1 \) is directly connected in parallel with a combination of series-connected \( C_2 \) and \( C_3 \). The voltage source \( V \) is applied across the entire setup.
### Steps to Analyze the Circuit:
1. **Identify the Configuration:**
- Capacitor \( C_1 \) is in parallel with the series combination of \( C_2 \) and \( C_3 \).
2. **Calculate the Equivalent Capacitance of Series Combination (C_2 and C_3):**
The formula to find the equivalent capacitance \( C_{\text{series}} \) for capacitors in series is:
\[
\frac{1}{C_{\text{series}}} = \frac{1}{C_2} + \frac{1}{C_3}
\]
Substituting the values:
\[
\frac{1}{C_{\text{series}}} = \frac{1}{330 \,\mu\text{F}} + \frac{1}{100 \,\mu\text{F}}
\]
Calculate the reciprocal to find \( C_{\text{series}} \).
3. **Calculate the Total Capacitance \( C_{\text{total}} \):**
Since \( C_1 \) is in parallel with the equivalent series capacitance \( C_{\text{series}} \):
\[
C_{\text{total}} = C_1 + C_{\text{series}}
\]
4. **Determine the Charge Stored on Each Capacitor:**
The charge \( Q \) on a capacitor is given by:
\[
Q = C \times V
\]
- Charge on \( C_1 \): \( Q_1 = C_1 \times V \)
- Find the voltage across](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71886d56-a83a-4d7b-8e18-9a0e9bdd4c82%2F599ac86f-b27d-46a3-88a4-2ad78ca4f098%2Fda3rf1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 4: Capacitor Circuit Analysis**
**Objective:**
Using the given circuit, where \( V = 6 \text{V} \), \( C_1 = 470 \,\mu\text{F} \), \( C_2 = 330 \,\mu\text{F} \), and \( C_3 = 100 \,\mu\text{F} \), determine the charges and energies stored on each capacitor.
**Description of the Circuit Diagram:**
The diagram depicts a circuit with three capacitors. Capacitor \( C_1 \) is directly connected in parallel with a combination of series-connected \( C_2 \) and \( C_3 \). The voltage source \( V \) is applied across the entire setup.
### Steps to Analyze the Circuit:
1. **Identify the Configuration:**
- Capacitor \( C_1 \) is in parallel with the series combination of \( C_2 \) and \( C_3 \).
2. **Calculate the Equivalent Capacitance of Series Combination (C_2 and C_3):**
The formula to find the equivalent capacitance \( C_{\text{series}} \) for capacitors in series is:
\[
\frac{1}{C_{\text{series}}} = \frac{1}{C_2} + \frac{1}{C_3}
\]
Substituting the values:
\[
\frac{1}{C_{\text{series}}} = \frac{1}{330 \,\mu\text{F}} + \frac{1}{100 \,\mu\text{F}}
\]
Calculate the reciprocal to find \( C_{\text{series}} \).
3. **Calculate the Total Capacitance \( C_{\text{total}} \):**
Since \( C_1 \) is in parallel with the equivalent series capacitance \( C_{\text{series}} \):
\[
C_{\text{total}} = C_1 + C_{\text{series}}
\]
4. **Determine the Charge Stored on Each Capacitor:**
The charge \( Q \) on a capacitor is given by:
\[
Q = C \times V
\]
- Charge on \( C_1 \): \( Q_1 = C_1 \times V \)
- Find the voltage across
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