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. `5P`
B. `1.5P`
C. `P`
D. `(2)/(5)P`

Explanation

To solve the problem, we need to understand the relationship between the primary and secondary coils in a transformer and how power is conserved in an ideal transformer (neglecting losses).

### Step-by-Step Solution:

1. **Understand the Transformer Turns Ratio**:
The transformer has a turns ratio of secondary to primary given as \( \frac{N_s}{N_p} = \frac{3}{2} \). This means for every 2 turns in the primary coil, there are 3 turns in the secondary coil.

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

3. **Given Output Power**:
We are given that the output power \( P_{out} = P \).

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

### Final Answer:
The input power neglecting all losses must be equal to \( P \).