### Capacitors in Series and Parallel with Breakdown Scenario#### Problem Statement:In the figure, a potential difference of \( V = 106 \) V is applied across a capacitor arrangement with capacitances:- \( C_1 = 10.7 \ \mu \text{F} \)- \( C_2 = 6.06 \ \mu \text{F} \)- \( C_3 = 4.66 \ \mu \text{F} \).If capacitor 3 undergoes electrical breakdown so that it becomes equivalent to conducting wire, what is the increase in:(a) the charge on capacitor 1, and (b) the potential difference across capacitor 1?#### Diagram Explanation:The given circuit diagram shows a series-parallel combination of three capacitors. The capacitors are labeled \( C_1 \), \( C_2 \), and \( C_3 \). The potential difference \( V \) is applied across the entire arrangement. Capacitor \( C_3 \) is in series with the parallel combination of capacitors \( C_1 \) and \( C_2 \).##### Capacitor Arrangement:- \( C_3 \) is in series with the parallel combination of \( C_1 \) and \( C_2 \).### Questions:(a) **Number** [Input Box] **Units** [Dropdown Menu](b) **Number** [Input Box] **Units** [Dropdown Menu]### Solution Approach:1. **Initial Configuration:** - Calculate the equivalent capacitance of capacitors \( C_1 \) and \( C_2 \) in parallel. - Then calculate the total equivalent capacitance of the resulting parallel capacitance in series with \( C_3 \).2. **Breakdown Event:** - Analyze the circuit assuming \( C_3 \) has become a conducting wire (i.e., short-circuited). - Recalculate the equivalent capacitance and the new charge and potential distribution.#### Notes:When a capacitor undergoes electrical breakdown and acts as a conducting wire, it essentially creates a short circuit at its position. This scenario will significantly affect the distribution of voltages and charge in the circuit.---This transcription is designed for educational use, explaining the problem statement, approach, and key points for the learners to understand how to solve the given capacitor network problem, especially under the condition of electrical breakdown.

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In the figure a potential difference of V = 106 V is applied across a capacitor arrangement with capacitances C₁ = 10.7 μF, C₂ = 6.06 µF, and C3 = 4.66 µF. If capacitor 3 undergoes electrical breakdown so that it becomes equivalent to conducting wire, what is the increase in (a) the charge on capacitor 1 and (b) the potential difference across capacitor 1? (a) Number i (b) Number i Units Units C3 C₂

In the figure a potential difference of V = 106 V is applied across a capacitor arrangement with capacitances C₁ = 10.7 μF, C₂ = 6.06 µF, and C3 = 4.66 µF. If capacitor 3 undergoes electrical breakdown so that it becomes equivalent to conducting wire, what is the increase in (a) the charge on capacitor 1 and (b) the potential difference across capacitor 1? (a) Number i (b) Number i Units Units C3 C₂

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

Combination of Capacitors

The connection of capacitors can be established in a circuit in two ways.

Question

### Capacitors in Series and Parallel with Breakdown Scenario

#### Problem Statement:
In the figure, a potential difference of \( V = 106 \) V is applied across a capacitor arrangement with capacitances:
- \( C_1 = 10.7 \ \mu \text{F} \)
- \( C_2 = 6.06 \ \mu \text{F} \)
- \( C_3 = 4.66 \ \mu \text{F} \).

If capacitor 3 undergoes electrical breakdown so that it becomes equivalent to conducting wire, what is the increase in:
(a) the charge on capacitor 1, and
(b) the potential difference across capacitor 1?

#### Diagram Explanation:
The given circuit diagram shows a series-parallel combination of three capacitors. The capacitors are labeled \( C_1 \), \( C_2 \), and \( C_3 \). The potential difference \( V \) is applied across the entire arrangement. Capacitor \( C_3 \) is in series with the parallel combination of capacitors \( C_1 \) and \( C_2 \).

##### Capacitor Arrangement:
- \( C_3 \) is in series with the parallel combination of \( C_1 \) and \( C_2 \).

### Questions:

(a) **Number** [Input Box] **Units** [Dropdown Menu]

(b) **Number** [Input Box] **Units** [Dropdown Menu]

### Solution Approach:
1. **Initial Configuration:**
- Calculate the equivalent capacitance of capacitors \( C_1 \) and \( C_2 \) in parallel.
- Then calculate the total equivalent capacitance of the resulting parallel capacitance in series with \( C_3 \).

2. **Breakdown Event:**
- Analyze the circuit assuming \( C_3 \) has become a conducting wire (i.e., short-circuited).
- Recalculate the equivalent capacitance and the new charge and potential distribution.

#### Notes:
When a capacitor undergoes electrical breakdown and acts as a conducting wire, it essentially creates a short circuit at its position. This scenario will significantly affect the distribution of voltages and charge in the circuit.

---

This transcription is designed for educational use, explaining the problem statement, approach, and key points for the learners to understand how to solve the given capacitor network problem, especially under the condition of electrical breakdown.

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