Four ways of making a network of five capacitor of the same value are shown in four choices. Three out of four are identical. The one which is different is

Options

A. `
B. `
C. `
D. `

Explanation

To solve the problem of identifying which of the four capacitor networks is different from the others, we will analyze each configuration step by step.

### Step-by-Step Solution:

1. **Understanding the Capacitor Configurations:**
- We have four configurations of five identical capacitors. We need to determine which one is different based on their arrangement.

2. **Identifying Wheatstone Bridge:**
- A Wheatstone bridge is a specific arrangement of resistors (or capacitors in this case) that allows for the balancing of the circuit. If the bridge is balanced, no current flows through the bridge, and the capacitors can be simplified.

3. **Analyzing the First Three Configurations (A, B, C):**
- For the first three configurations (let's call them A, B, and C), we check if they form a Wheatstone bridge.
- If they do, we can simplify the circuit by ignoring the branch that does not affect the overall capacitance.

4. **Calculating Capacitance for A, B, and C:**
- Assume each capacitor has a capacitance value of C.
- In each configuration, we can group the capacitors into series and parallel combinations.
- For example, if two capacitors are in series, the equivalent capacitance \(C_{eq}\) is given by:
\[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} \]
- If two capacitors are in parallel, the equivalent capacitance is:
\[ C_{eq} = C_1 + C_2 \]

5. **Finding the Equivalent Capacitance:**
- For configurations A, B, and C, after simplification, we find that the net capacitance is the same (let's say it equals C).

6. **Analyzing the Fourth Configuration (D):**
- Now we check the fourth configuration (D) to see if it forms a Wheatstone bridge.
- If it does not form a Wheatstone bridge, the current will flow through the bridge, and the capacitors cannot be simplified in the same way.

7. **Conclusion:**
- Since configurations A, B, and C are identical and follow Wheatstone bridge balancing, while configuration D does not, we conclude that option D is the different one.

### Final Answer:
The configuration that is different is **option D**.

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