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

Options

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

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Number of turns in the primary winding (N_p) = 500 turns
- Number of turns in the secondary winding (N_s) = 5000 turns
- Voltage of the primary coil (V_p) = 20 V

2. **Write the Transformer Equation:**
The relationship between the primary and secondary voltages and the number of turns is given by the formula:
\[ \frac{N_s}{N_p} = \frac{V_s}{V_p} \]
where:
- \(N_s\) = number of turns in the secondary winding
- \(N_p\) = number of turns in the primary winding
- \(V_s\) = voltage in the secondary winding
- \(V_p\) = voltage in the primary winding

3. **Substitute the Known Values into the Equation:**
\[ \frac{5000}{500} = \frac{V_s}{20} \]

4. **Simplify the Left Side:**
\[ 10 = \frac{V_s}{20} \]

5. **Solve for \(V_s\):**
To find \(V_s\), multiply both sides by 20:
\[ V_s = 10 \times 20 = 200 \, \text{V} \]

6. **Determine the Frequency:**
The frequency of the secondary voltage remains the same as that of the primary voltage, which is given as 50 Hz.

7. **Final Result:**
The output voltage in the secondary winding is \(V_s = 200 \, \text{V}\) and the frequency is 50 Hz.

### Conclusion:
The secondary will have an output of **200 V** at **50 Hz**.

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