The number of turns of primary and secondary coils of a transformer are 5 and 10 respectively and the mutual inductance of the tranformar is 25 henry. Now the number of turns in the primary and secondary of the transformar are made 10 and 5 respectivaly. The mutual inductance of the transformar in henry will be

Options

A. `6.25`
B. `12.5`
C. 25
D. 50

Answer

To solve the problem, we need to understand how mutual inductance changes with the number of turns in the primary and secondary coils of a transformer.

### Given:
- Number of turns in the primary coil (N_p1) = 5
- Number of turns in the secondary coil (N_s1) = 10
- Mutual inductance in the first case (M1) = 25 Henry

Now, in the second case:
- Number of turns in the primary coil (N_p2) = 10
- Number of turns in the secondary coil (N_s2) = 5

### Step-by-Step Solution:

1. **Understand the relationship of mutual inductance with the number of turns**:
The mutual inductance (M) of a transformer is directly proportional to the product of the number of turns in the primary and secondary coils:
\[ M \propto N_p \times N_s \]

2. **Calculate the product of the number of turns for the first case**:
\[ N_p1 \times N_s1 = 5 \times 10 = 50 \]

3. **Calculate the product of the number of turns for the second case**:
\[ N_p2 \times N_s2 = 10 \times 5 = 50 \]

4. **Compare the products of the number of turns**:
Since the product \(N_p \times N_s\) is the same in both cases (50), we can conclude that the mutual inductance will remain the same.

5. **Determine the mutual inductance for the second case**:
Since the product of the number of turns is the same, the mutual inductance (M2) in the second case will be equal to M1:
\[ M2 = M1 = 25 \text{ Henry} \]

### Final Answer:
The mutual inductance of the transformer in the second case is **25 Henry**.

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