A common transistor radio set requires 12V (D.C.) for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V (A.C.) on standard domestic A.C. supply. The number of turns of secondary coil are 24, then the number of turns of primary are ______.

Answer

To solve the problem, we need to find the number of turns in the primary coil (Np) of a transformer given the number of turns in the secondary coil (Ns) and the voltages across the primary (Vp) and secondary (Vs) coils.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Voltage across the primary (Vp) = 220 V (AC)
- Voltage across the secondary (Vs) = 12 V (DC)
- Number of turns in the secondary coil (Ns) = 24 turns

2. **Use the Transformer Turn Ratio Formula:**
The relationship between the number of turns and the voltages in a transformer is given by the formula:
\[ \frac{N_p}{N_s} = \frac{V_p}{V_s} \]
Where:
- \(N_p\) = Number of turns in the primary coil
- \(N_s\) = Number of turns in the secondary coil
- \(V_p\) = Voltage in the primary coil
- \(V_s\) = Voltage in the secondary coil

3. **Substitute the Known Values:**
Substitute the known values into the formula:
\[ \frac{N_p}{24} = \frac{220}{12} \]

4. **Cross-Multiply to Solve for \(N_p\):**
To find \(N_p\), we can cross-multiply:
\[ N_p = 24 \times \frac{220}{12} \]

5. **Calculate \(N_p\):**
First, simplify \(\frac{220}{12}\):
\[ \frac{220}{12} = \frac{55}{3} \approx 18.33 \]
Now, multiply by 24:
\[ N_p = 24 \times 18.33 \approx 440 \]

6. **Final Answer:**
The number of turns in the primary coil (Np) is approximately 440.

### Final Result:
The number of turns of the primary coil is **440**.

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