A power transmission line feeds input power at 2400 V to a step down transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary windings in order to get output power at 240 V?

Options

A. 400
B. 420
C. 424
D. 436

Answer

To solve the problem of finding the number of turns in the secondary winding of a step-down transformer, we can use the transformer equation which relates the primary and secondary voltages to the number of turns in the primary and secondary coils.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Primary Voltage (\( V_p \)): 2400 V
- Secondary Voltage (\( V_s \)): 240 V
- Number of Turns in Primary (\( N_p \)): 4000 turns

2. **Write the Transformer Equation:**
The transformer equation is given by:
\[ \frac{V_p}{N_p} = \frac{V_s}{N_s} \]
Where:
- \( V_p \) = Primary Voltage
- \( N_p \) = Number of turns in the primary winding
- \( V_s \) = Secondary Voltage
- \( N_s \) = Number of turns in the secondary winding

3. **Rearrange the Equation to Solve for \( N_s \):**
Rearranging the equation to find \( N_s \):
\[ N_s = \frac{V_s \cdot N_p}{V_p} \]

4. **Substitute the Known Values:**
Now substitute the known values into the equation:
\[ N_s = \frac{240 \, \text{V} \cdot 4000 \, \text{turns}}{2400 \, \text{V}} \]

5. **Calculate \( N_s \):**
Simplifying the equation:
\[ N_s = \frac{240 \cdot 4000}{2400} \]
\[ N_s = \frac{960000}{2400} \]
\[ N_s = 400 \, \text{turns} \]

### Final Answer:
The number of turns in the secondary winding should be **400 turns**.

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