In a transformer the output current and voltage are respectively `4 A` and `20V`. If the ratio of number of turns in the primary to secondary is `2:1` what is the input current and voltage?

Options

A. `2A` and `40V`
B. `8A` and `10V`
C. `4A` and `10V`
D. `8A` and `40V`

Explanation

To solve the problem, we will use the relationships in a transformer regarding the number of turns, voltage, and current.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Output Current (Secondary Current, \( I_s \)) = 4 A
- Output Voltage (Secondary Voltage, \( V_s \)) = 20 V
- Ratio of number of turns in the primary to secondary (\( \frac{N_p}{N_s} \)) = 2:1

2. **Calculate Input Voltage (\( V_p \)):**
- The relationship between the primary and secondary voltages and the number of turns is given by:
\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]
- Rearranging this gives:
\[ V_p = \frac{N_p}{N_s} \times V_s \]
- Substituting the known values:
\[ V_p = 2 \times 20 \, \text{V} = 40 \, \text{V} \]

3. **Calculate Input Current (\( I_p \)):**
- The relationship between the primary and secondary currents and the number of turns is given by:
\[ \frac{I_p}{I_s} = \frac{N_s}{N_p} \]
- Rearranging this gives:
\[ I_p = \frac{N_s}{N_p} \times I_s \]
- Substituting the known values:
\[ I_p = \frac{1}{2} \times 4 \, \text{A} = 2 \, \text{A} \]

### Final Answers:
- Input Voltage (\( V_p \)) = 40 V
- Input Current (\( I_p \)) = 2 A