The primary winding of transformer has `500` turns whereas its secondary has `5000` turns. The primary is connected to an ac supply of `20V,50Hz`. The secondary will have an output of
(1.)2 V , 5 H z
(2.)200 V , 500 H z
(3.)2 V , 50 H z
(4.)200 V , 50 H z

Options

A. `2V,5Hz`
B. `200V,500Hz`
C. `2V,50Hz`
D. `200V,50Hz`

Answer

To solve the problem, we will use the transformer equation that relates the primary and secondary voltages and the number of turns in the primary and secondary windings.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Number of turns in the primary winding, \( N_p = 500 \)
- Number of turns in the secondary winding, \( N_s = 5000 \)
- Voltage in the primary winding, \( V_p = 20 \, \text{V} \)
- Frequency of the AC supply, \( f = 50 \, \text{Hz} \)

2. **Use the Transformer Equation:**
The relationship between the primary and secondary voltages and the number of turns is given by:
\[ \frac{N_s}{N_p} = \frac{V_s}{V_p} \]
Where:
- \( V_s \) = Secondary voltage
- \( V_p \) = Primary voltage

3. **Rearranging the Equation:**
To find the secondary voltage \( V_s \), we can rearrange the equation:
\[ V_s = \frac{N_s}{N_p} \times V_p \]

4. **Substituting the Values:**
Now, substitute the known values into the equation:
\[ V_s = \frac{5000}{500} \times 20 \]

5. **Calculating the Secondary Voltage:**
Simplifying the fraction:
\[ V_s = 10 \times 20 = 200 \, \text{V} \]

6. **Determine the Frequency:**
The frequency of the output voltage in the secondary winding remains the same as that of the primary winding, which is:
\[ f_s = f_p = 50 \, \text{Hz} \]

7. **Final Result:**
Therefore, the output of the secondary will be:
\[ V_s = 200 \, \text{V}, \quad f_s = 50 \, \text{Hz} \]

### Conclusion:
The correct answer is option (4): **200 V, 50 Hz**.

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