the figure below, V = 12V, C1 = 10μF, C2 = 20μF, and C3 = 30μF. Assume the voltage source V as been connected for a long time (so all the capacitors are fully charged). (a) What is the equivalent capacitance of the entire circuit? (b) What is the charge on each capacitor if they are fully charged? (c) What is the potential difference across each capacitor if they are fully charged? (d) What is the potential energy stored in each capacitor when they are fully charged?

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In the figure below, V = 12V, C1 = 10μF, C2 = 20μF, and C3 = 30μF. Assume the voltage source V as been connected for a long time (so all the capacitors are fully charged). (a) What is the equivalent capacitance of the entire circuit? (b) What is the charge on each capacitor if they are fully charged? (c) What is the potential difference across each capacitor if they are fully charged? (d) What is the potential energy stored in each capacitor when they are fully charged?
The diagram represents an electrical circuit with three capacitors. 

- **Capacitors Configuration:**
  - Capacitors \( C_1 \) and \( C_2 \) are connected in parallel.
  - The combination of \( C_1 \) and \( C_2 \) is connected in series with capacitor \( C_3 \).

- **Voltage Source:**
  - The voltage across the entire circuit is labeled as \( V \).

**Explanation of Circuit:**

1. **Parallel Capacitors:** The capacitors \( C_1 \) and \( C_2 \) share the same voltage across their terminals. The total capacitance for capacitors in parallel is given by the sum of their capacitances:
   \[
   C_{\text{parallel}} = C_1 + C_2
   \]

2. **Series Capacitor:** The equivalent parallel capacitance \( C_{\text{parallel}} \) is connected in series with \( C_3 \). For capacitors in series, the total capacitance \( C_{\text{total}} \) is calculated using the reciprocal formula:
   \[
   \frac{1}{C_{\text{total}}} = \frac{1}{C_{\text{parallel}}} + \frac{1}{C_3}
   \]

This circuit is a basic example often used to illustrate how capacitance is calculated for combined series and parallel connections in electrical engineering.
Transcribed Image Text:The diagram represents an electrical circuit with three capacitors. - **Capacitors Configuration:** - Capacitors \( C_1 \) and \( C_2 \) are connected in parallel. - The combination of \( C_1 \) and \( C_2 \) is connected in series with capacitor \( C_3 \). - **Voltage Source:** - The voltage across the entire circuit is labeled as \( V \). **Explanation of Circuit:** 1. **Parallel Capacitors:** The capacitors \( C_1 \) and \( C_2 \) share the same voltage across their terminals. The total capacitance for capacitors in parallel is given by the sum of their capacitances: \[ C_{\text{parallel}} = C_1 + C_2 \] 2. **Series Capacitor:** The equivalent parallel capacitance \( C_{\text{parallel}} \) is connected in series with \( C_3 \). For capacitors in series, the total capacitance \( C_{\text{total}} \) is calculated using the reciprocal formula: \[ \frac{1}{C_{\text{total}}} = \frac{1}{C_{\text{parallel}}} + \frac{1}{C_3} \] This circuit is a basic example often used to illustrate how capacitance is calculated for combined series and parallel connections in electrical engineering.
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