The ratio of secondary to the primary turns in a transformer is `3:2`. If the power output be `P`, then the input power neglecting all loses must be equal to

Options

A. 0.70833333333333
B. 1.5 P
C. P
D. (2/5)P

Explanation

To solve the problem, we need to understand the relationship between the primary and secondary turns in a transformer and how it relates to the power input and output.

### Step-by-Step Solution:

1. **Understand the Transformer Turns Ratio**:
The turns ratio of a transformer is given as \( \frac{N_s}{N_p} = \frac{3}{2} \), where \( N_s \) is the number of turns in the secondary coil and \( N_p \) is the number of turns in the primary coil.

2. **Power Relationship in a Transformer**:
In an ideal transformer (neglecting losses), the power input to the transformer is equal to the power output. This can be expressed as:
\[ P_{in} = P_{out} \]
where \( P_{in} \) is the input power and \( P_{out} \) is the output power.

3. **Given Output Power**:
According to the problem, the output power \( P_{out} \) is given as \( P \).

4. **Calculate Input Power**:
Since we are neglecting all losses, the input power must also be equal to the output power. Therefore:
\[ P_{in} = P \]

5. **Conclusion**:
The input power, neglecting all losses, must be equal to \( P \).

### Final Answer:
Thus, the input power must be equal to \( P \).

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