The current in the primary circuit and secondary circuit of a transformer are 20 A and 4 A respectively. If the number of turns in primary coil is 560. What is the number of turns in secondary circuit if the transformer has 100% efficiency?

Options

A. 112
B. 280
C. 1120
D. 2800

Explanation

To solve the problem, we need to use the relationship between the currents and the number of turns in the primary and secondary coils of a transformer. The formula for an ideal transformer is given by:

\[ \frac{I_p}{I_s} = \frac{N_s}{N_p} \]

Where:
- \(I_p\) = Current in the primary circuit
- \(I_s\) = Current in the secondary circuit
- \(N_p\) = Number of turns in the primary coil
- \(N_s\) = Number of turns in the secondary coil

Given data:
- \(I_p = 20 \, A\)
- \(I_s = 4 \, A\)
- \(N_p = 560\)

We need to find \(N_s\).

### Step-by-step Solution:

1. **Write down the known values**:
- Primary current \(I_p = 20 \, A\)
- Secondary current \(I_s = 4 \, A\)
- Number of turns in primary \(N_p = 560\)

2. **Use the transformer equation**:
\[ \frac{I_p}{I_s} = \frac{N_s}{N_p} \]

3. **Substitute the known values into the equation**:
\[ \frac{20}{4} = \frac{N_s}{560} \]

4. **Simplify the left side**:
\[ 5 = \frac{N_s}{560} \]

5. **Cross-multiply to solve for \(N_s\)**:
\[ N_s = 5 \times 560 \]

6. **Calculate \(N_s\)**:
\[ N_s = 2800 \]

### Final Answer:
The number of turns in the secondary circuit \(N_s\) is **2800**.