Refer to the diagram. Both capacitors are fully charged. Find the potential of the conducting surface indicated in the diagram (which is the conducting surface between the two capacitors, the bottom of the top capacitor and the top of the bottom capacitor). It is not okay to use some formula you memorized for two capacitors in series, but here is a hint: think about what the net charge would have to be on that conducting surface between the two capacitors.

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 Refer to the diagram. Both capacitors are fully charged. Find the potential of the conducting surface indicated in the diagram (which is the conducting surface between the two capacitors, the bottom of the top capacitor and the top of the bottom capacitor). It is not okay to use some formula you memorized for two capacitors in series, but here is a hint: think about what the net charge would have to be on that conducting surface between the two capacitors.

### Circuit Analysis with Fully Charged Capacitors

In this diagram, we analyze a circuit with fully charged capacitors. The circuit includes three resistors, two capacitors, and a power source. Here's a detailed breakdown of the components and connections:

#### Components:
1. **Voltage Source (E):** 10V
2. **Resistors:**
   - \( R_1 = 5 \Omega \)
   - \( R_2 = 5 \Omega \)
   - \( R_3 = 5 \Omega \)
3. **Capacitors:**
   - \( C_1 = 1 \text{F} \)
   - \( C_2 = 2 \text{F} \)

#### Circuit Description:
- The circuit starts with a voltage source (E) of 10V.
- The voltage source is connected in series with resistor \( R_1 \) (5Ω).
- Following \( R_1 \), the circuit splits into two parallel branches:
  1. The first branch contains resistor \( R_2 \) (5Ω).
  2. The second branch contains resistor \( R_3 \) (5Ω) in series with two capacitors \( C_1 \) (1F) and \( C_2 \) (2F) in series.

#### Key Analysis Points:
- **Fully Charged Capacitors:** Both \( C_1 \) and \( C_2 \) are fully charged, implying that there is no current flowing through the capacitors.
- **Voltage Calculation (V):** The voltage across the capacitors needs to be determined (denoted as \( V \)).

To find \( V \), consider the implications of fully charged capacitors:
1. Once fully charged, capacitors in a DC circuit act as open circuits.
2. The voltage across each capacitor depends on its capacitance and the total voltage provided by the source.

Given \( C_1 \) and \( C_2 \) are in series:
- The equivalent capacitance \( C_{eq} = \frac{1}{\frac{1}{C_1} + \frac{1}{C_2}} = \frac{1}{\frac{1}{1} + \frac{1}{2}} = \frac{1}{1.5} = \frac{2}{3} \text{ F} \)
- Using
Transcribed Image Text:### Circuit Analysis with Fully Charged Capacitors In this diagram, we analyze a circuit with fully charged capacitors. The circuit includes three resistors, two capacitors, and a power source. Here's a detailed breakdown of the components and connections: #### Components: 1. **Voltage Source (E):** 10V 2. **Resistors:** - \( R_1 = 5 \Omega \) - \( R_2 = 5 \Omega \) - \( R_3 = 5 \Omega \) 3. **Capacitors:** - \( C_1 = 1 \text{F} \) - \( C_2 = 2 \text{F} \) #### Circuit Description: - The circuit starts with a voltage source (E) of 10V. - The voltage source is connected in series with resistor \( R_1 \) (5Ω). - Following \( R_1 \), the circuit splits into two parallel branches: 1. The first branch contains resistor \( R_2 \) (5Ω). 2. The second branch contains resistor \( R_3 \) (5Ω) in series with two capacitors \( C_1 \) (1F) and \( C_2 \) (2F) in series. #### Key Analysis Points: - **Fully Charged Capacitors:** Both \( C_1 \) and \( C_2 \) are fully charged, implying that there is no current flowing through the capacitors. - **Voltage Calculation (V):** The voltage across the capacitors needs to be determined (denoted as \( V \)). To find \( V \), consider the implications of fully charged capacitors: 1. Once fully charged, capacitors in a DC circuit act as open circuits. 2. The voltage across each capacitor depends on its capacitance and the total voltage provided by the source. Given \( C_1 \) and \( C_2 \) are in series: - The equivalent capacitance \( C_{eq} = \frac{1}{\frac{1}{C_1} + \frac{1}{C_2}} = \frac{1}{\frac{1}{1} + \frac{1}{2}} = \frac{1}{1.5} = \frac{2}{3} \text{ F} \) - Using
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