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`

Explanation

To solve the problem, we will use the relationship between mutual inductance and the number of turns in the coils of a transformer. The mutual inductance \( M \) is directly proportional to the product of the number of turns in the primary coil \( N_P \) and the number of turns in the secondary coil \( N_S \).

### Step-by-Step Solution:

1. **Identify the initial conditions:**
- Number of turns in the primary coil (initial): \( N_{P1} = 5 \)
- Number of turns in the secondary coil (initial): \( N_{S1} = 10 \)
- Mutual inductance (initial): \( M_1 = 25 \, \text{H} \)

2. **Calculate the product of turns for the initial configuration:**
\[ P_1 = N_{P1} \times N_{S1} = 5 \times 10 = 50 \]

3. **Identify the new conditions:**
- Number of turns in the primary coil (new): \( N_{P2} = 10 \)
- Number of turns in the secondary coil (new): \( N_{S2} = 5 \)

4. **Calculate the product of turns for the new configuration:**
\[ P_2 = N_{P2} \times N_{S2} = 10 \times 5 = 50 \]

5. **Relate mutual inductance to the product of turns:**
Since mutual inductance \( M \) is proportional to the product of the number of turns, we can write:
\[ M \propto P \]
Thus, if \( P_1 = P_2 \), then \( M_1 = M_2 \).

6. **Conclude the mutual inductance for the new configuration:**
Since \( P_1 = P_2 \) (both equal to 50), the mutual inductance remains the same:
\[ M_2 = M_1 = 25 \, \text{H} \]

### Final Answer:
The mutual inductance of the transformer when the number of turns in the primary and secondary coils are changed to 10 and 5 respectively will still be \( 25 \, \text{H} \).

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