A `100%` efficient transformer has `100` turns in the primary and `25` turns in its secondary coil. Of the current in the secondary coil is `4` amp, then the current in the primary coil is

Options

A. `1` amp
B. `4` amp
C. `8` amp
D. `16` amp

Explanation

To solve the problem of finding the current in the primary coil of a transformer given the current in the secondary coil, we can use the principles of electromagnetic induction and the relationships between the turns in the coils and the currents.

### Step-by-Step Solution:

1. **Understand the Transformer Basics**:
A transformer operates on the principle of electromagnetic induction and consists of two coils: the primary coil and the secondary coil. The number of turns in each coil affects the voltage and current relationship.

2. **Identify Given Values**:
- Number of turns in the primary coil, \( N_p = 100 \)
- Number of turns in the secondary coil, \( N_s = 25 \)
- Current in the secondary coil, \( I_s = 4 \, \text{A} \)

3. **Use the Transformer Equation**:
For an ideal transformer (100% efficiency), the relationship between the primary and secondary currents and turns is given by:
\[ \frac{N_p}{N_s} = \frac{I_s}{I_p} \]
where \( I_p \) is the current in the primary coil.

4. **Substitute the Known Values**:
Plugging in the values we have:
\[ \frac{100}{25} = \frac{4}{I_p} \]

5. **Simplify the Ratio**:
The left side simplifies to:
\[ 4 = \frac{4}{I_p} \]

6. **Cross-Multiply to Solve for \( I_p \)**:
Cross-multiplying gives:
\[ 4 \cdot I_p = 4 \]

7. **Solve for \( I_p \)**:
Dividing both sides by 4:
\[ I_p = 1 \, \text{A} \]

### Final Answer:
The current in the primary coil is \( 1 \, \text{A} \).

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