What are the charge on and the potential difference across each capacitor in figure own? C, : :5 µF +4 µF 9 V C3 + 6 µF

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### Electrical Capacitors in Circuits: Understanding Charge and Potential Difference

#### Diagram Analysis

The provided diagram illustrates a circuit containing a 9-volt (V) battery connected to three capacitors. The three capacitors are arranged as follows:

- **C1 (5 µF)** capacitor is directly in series with the battery.
- **C2 (4 µF)** and **C3 (6 µF)** capacitors are connected in parallel with each other.

#### Problem Statement

The question asks us to determine:
- The charge on each capacitor.
- The potential difference (voltage) across each capacitor.

#### Calculation Methodology

1. **Calculate the Equivalent Capacitance of C2 and C3 (Parallel Combination):**
   - For capacitors in parallel: \(C_{parallel} = C_2 + C_3\)
     \[
     C_{parallel} = 4\, \mu F + 6\, \mu F = 10\, \mu F
     \]

2. **Combine C1 with the Parallel Capacitance (Series Combination):**
   - For capacitors in series: \(\frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_{parallel}}\)
     \[
     \frac{1}{C_{total}} = \frac{1}{5\, \mu F} + \frac{1}{10\, \mu F} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10}
     \]
     \[
     C_{total} = \frac{10}{3} \mu F = 3.33 \mu F
     \]

3. **Calculate the Charge using the Total Capacitance:**
   - Using the formula \(Q = CV\) where \(Q\) is charge, \(C\) is capacitance, and \(V\) is voltage:
     \[
     Q_{total} = C_{total} \times 9V = 3.33\, \mu F \times 9\, V = 30\, \mu C
     \]

4. **Voltage Across C1:**
   - Since \(Q = CV\):
     \[
     V_1 = \frac{Q_{total}}{C_1} = \frac{30\, \mu C}{5\,
Transcribed Image Text:### Electrical Capacitors in Circuits: Understanding Charge and Potential Difference #### Diagram Analysis The provided diagram illustrates a circuit containing a 9-volt (V) battery connected to three capacitors. The three capacitors are arranged as follows: - **C1 (5 µF)** capacitor is directly in series with the battery. - **C2 (4 µF)** and **C3 (6 µF)** capacitors are connected in parallel with each other. #### Problem Statement The question asks us to determine: - The charge on each capacitor. - The potential difference (voltage) across each capacitor. #### Calculation Methodology 1. **Calculate the Equivalent Capacitance of C2 and C3 (Parallel Combination):** - For capacitors in parallel: \(C_{parallel} = C_2 + C_3\) \[ C_{parallel} = 4\, \mu F + 6\, \mu F = 10\, \mu F \] 2. **Combine C1 with the Parallel Capacitance (Series Combination):** - For capacitors in series: \(\frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_{parallel}}\) \[ \frac{1}{C_{total}} = \frac{1}{5\, \mu F} + \frac{1}{10\, \mu F} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10} \] \[ C_{total} = \frac{10}{3} \mu F = 3.33 \mu F \] 3. **Calculate the Charge using the Total Capacitance:** - Using the formula \(Q = CV\) where \(Q\) is charge, \(C\) is capacitance, and \(V\) is voltage: \[ Q_{total} = C_{total} \times 9V = 3.33\, \mu F \times 9\, V = 30\, \mu C \] 4. **Voltage Across C1:** - Since \(Q = CV\): \[ V_1 = \frac{Q_{total}}{C_1} = \frac{30\, \mu C}{5\,
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