In a transformer,`n_(p) = 500,n_(s) = 5000` Input voltage is 20 V and frequency is 50 Hz. Then in the output, we have

Options

A. 200 V, 500 Hz
B. 200 V, 50 Hz
C. 20 V, 50 Hz
D. 2V, 5 Hz.

Explanation

To solve the problem, we need to find the output voltage and output frequency of the transformer given the number of turns in the primary and secondary coils, the input voltage, and the frequency.

### Step-by-Step Solution:

1. **Identify the given values:**
- Number of turns in the primary coil, \( n_p = 500 \)
- Number of turns in the secondary coil, \( n_s = 5000 \)
- Input voltage, \( V_p = 20 \, \text{V} \)
- Frequency, \( f = 50 \, \text{Hz} \)

2. **Understand the transformer relationship:**
The relationship between the primary voltage (\( V_p \)), secondary voltage (\( V_s \)), number of turns in the primary (\( n_p \)), and number of turns in the secondary (\( n_s \)) is given by the formula:
\[ \frac{V_p}{V_s} = \frac{n_p}{n_s} \]
Rearranging this formula gives us:
\[ V_s = V_p \times \frac{n_s}{n_p} \]

3. **Substitute the known values into the equation:**
\[ V_s = 20 \, \text{V} \times \frac{5000}{500} \]

4. **Calculate the output voltage:**
\[ V_s = 20 \, \text{V} \times 10 = 200 \, \text{V} \]

5. **Determine the output frequency:**
In a transformer, the frequency of the output voltage is the same as the frequency of the input voltage. Therefore:
\[ f_s = f_p = 50 \, \text{Hz} \]

6. **Final Result:**
The output voltage is \( 200 \, \text{V} \) and the output frequency is \( 50 \, \text{Hz} \).

### Summary:
- Output Voltage: \( 200 \, \text{V} \)
- Output Frequency: \( 50 \, \text{Hz} \)