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. 2C, 5 Hz.

Explanation

To solve the problem step by step, we will determine the output voltage and output frequency of the transformer based on the given parameters.

### Step 1: Identify the Given Values
- Number of primary coils, \( n_p = 500 \)
- Number of secondary coils, \( n_s = 5000 \)
- Input voltage, \( V_p = 20 \, \text{V} \)
- Frequency, \( f = 50 \, \text{Hz} \)

### Step 2: Determine the Output Frequency
In a transformer, the frequency of the output voltage remains the same as the input frequency. Therefore:
\[ f_s = f_p = 50 \, \text{Hz} \]

### Step 3: Use the Transformer Voltage Relation
The relationship between the primary and secondary voltages in a transformer is given by:
\[ \frac{V_s}{V_p} = \frac{n_s}{n_p} \]
Where:
- \( V_s \) = Output voltage
- \( V_p \) = Input voltage

### Step 4: Rearrange the Equation to Find Output Voltage
We can rearrange the equation to solve for \( V_s \):
\[ V_s = V_p \times \frac{n_s}{n_p} \]

### Step 5: Substitute the Known Values
Now, substitute the known values into the equation:
\[ V_s = 20 \, \text{V} \times \frac{5000}{500} \]

### Step 6: Calculate the Output Voltage
Calculating the fraction:
\[ \frac{5000}{500} = 10 \]
Now substitute back:
\[ V_s = 20 \, \text{V} \times 10 = 200 \, \text{V} \]

### Conclusion
- The output voltage \( V_s \) is \( 200 \, \text{V} \).
- The output frequency \( f_s \) is \( 50 \, \text{Hz} \).

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