A parallel plate capacitor has `91` plates, all are identical and arranged with same spacing between them. If the capacitance between adjacent plates is 3 pF. What will be the resultant capacitance?

Options

A. 273 pF
B. 30 pF
C. 94 pF
D. 270 pF

Answer

To solve the problem of finding the resultant capacitance of a parallel plate capacitor with 91 plates, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- A parallel plate capacitor consists of two plates. In this case, we have 91 plates arranged in parallel.
- Each adjacent pair of plates forms a capacitor.

2. **Determining the Number of Capacitors**:
- If there are 91 plates, the number of capacitors formed between adjacent plates is given by the formula:
\[ \text{Number of Capacitors} = \text{Number of Plates} - 1 \]
- Therefore, the number of capacitors is:
\[ 91 - 1 = 90 \]

3. **Given Capacitance of Each Capacitor**:
- The capacitance between each pair of adjacent plates is given as:
\[ C = 3 \text{ pF} \]

4. **Calculating the Total Capacitance**:
- Since all capacitors are in parallel, the total capacitance \(C_{total}\) is the sum of the capacitances of all the individual capacitors:
\[ C_{total} = C_1 + C_2 + C_3 + \ldots + C_{90} \]
- Since each capacitor has the same capacitance, we can simplify this to:
\[ C_{total} = 90 \times C \]
- Substituting the value of \(C\):
\[ C_{total} = 90 \times 3 \text{ pF} = 270 \text{ pF} \]

5. **Final Result**:
- The resultant capacitance of the system is:
\[ C_{total} = 270 \text{ pF} \]

### Conclusion:
The resultant capacitance of the parallel plate capacitor with 91 plates, where the capacitance between adjacent plates is 3 pF, is **270 pF**.

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