The circuit of the figure shows a capacitor, two ideal batteries, two resistors, and a switch S. Initially S has been open for a long time. If it is then closed for a long time, what is the change in the charge on the capacitor? Assume C = 36 μF, ₁ = 3.8V, E₂ = 3.0 V, R₁ = 0.500, and R₂ = 0.65 0.

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**Problem Statement:**

The circuit in the figure shows a capacitor, two ideal batteries, two resistors, and a switch \( S \). Initially, \( S \) has been open for a long time. If it is then closed for a long time, what is the change in the charge on the capacitor? Assume 
\[ C = 36 \mu F \]
\[ \mathcal{E}_1 = 3.8 V \]
\[ \mathcal{E}_2 = 3.0 V \]
\[ R_1 = 0.50 \Omega \]
\[ R_2 = 0.65 \Omega \]

**Circuit Diagram Explanation:**

The circuit diagram accompanying the problem statement consists of the following components:

1. **Capacitor (C):** Depicted as two parallel lines with a gap between them, symbolizing its ability to store charge.
2. **Switch (S):** Shown in series with the voltage source \(\mathcal{E}_1\) and resistor \(R_1\), indicating it can open or close the circuit.
3. **Voltage Sources (\(\mathcal{E}_1\) and \(\mathcal{E}_2\)):** Represented as cells or batteries, each providing a constant voltage of 3.8 V and 3.0 V respectively.
4. **Resistors (R1 and R2):** Symbolized with a zigzag pattern, indicating resistance values of 0.50 \(\Omega\) and 0.65 \(\Omega\) respectively.

The voltage source \(\mathcal{E}_1\) and resistor \(R_1\) form one branch of the circuit, while the voltage source \(\mathcal{E}_2\) and resistor \(R_2\) form a parallel branch. The capacitor \(C\) is located between these two branches.

**Question:**

Number: [__]

Units: [__]

**Instructions:**

- Determine the change in the charge on the capacitor when the switch \( S \) is closed for a long time.
- Enter the numerical value of the change in charge in the "Number" field.
- Choose the appropriate unit for the charge (likely coulombs) from the "Units" dropdown menu.
Transcribed Image Text:**Problem Statement:** The circuit in the figure shows a capacitor, two ideal batteries, two resistors, and a switch \( S \). Initially, \( S \) has been open for a long time. If it is then closed for a long time, what is the change in the charge on the capacitor? Assume \[ C = 36 \mu F \] \[ \mathcal{E}_1 = 3.8 V \] \[ \mathcal{E}_2 = 3.0 V \] \[ R_1 = 0.50 \Omega \] \[ R_2 = 0.65 \Omega \] **Circuit Diagram Explanation:** The circuit diagram accompanying the problem statement consists of the following components: 1. **Capacitor (C):** Depicted as two parallel lines with a gap between them, symbolizing its ability to store charge. 2. **Switch (S):** Shown in series with the voltage source \(\mathcal{E}_1\) and resistor \(R_1\), indicating it can open or close the circuit. 3. **Voltage Sources (\(\mathcal{E}_1\) and \(\mathcal{E}_2\)):** Represented as cells or batteries, each providing a constant voltage of 3.8 V and 3.0 V respectively. 4. **Resistors (R1 and R2):** Symbolized with a zigzag pattern, indicating resistance values of 0.50 \(\Omega\) and 0.65 \(\Omega\) respectively. The voltage source \(\mathcal{E}_1\) and resistor \(R_1\) form one branch of the circuit, while the voltage source \(\mathcal{E}_2\) and resistor \(R_2\) form a parallel branch. The capacitor \(C\) is located between these two branches. **Question:** Number: [__] Units: [__] **Instructions:** - Determine the change in the charge on the capacitor when the switch \( S \) is closed for a long time. - Enter the numerical value of the change in charge in the "Number" field. - Choose the appropriate unit for the charge (likely coulombs) from the "Units" dropdown menu.
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