If a transfomer of an audio amplifier has output impedance `8000Omega` and the speaker has input impedance of `8Omega`, the primary and secondary turns of this transfomer connected between the output of amplifier and to loud speaker should have the ratio

Options

A. `1000:1`
B. `100:1`
C. `1:32`
D. `32:1`

Answer

To solve the problem of finding the turns ratio of the transformer connected between the output of an audio amplifier and the loudspeaker, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Output impedance of the amplifier (primary impedance, \( R_p \)) = 8000 Ω
- Input impedance of the speaker (secondary impedance, \( R_s \)) = 8 Ω

2. **Use the transformer impedance relationship:**
The relationship between the primary and secondary impedances of a transformer is given by:
\[ \frac{R_p}{R_s} = \left(\frac{N_1}{N_2}\right)^2 \]
where \( N_1 \) is the number of turns in the primary coil and \( N_2 \) is the number of turns in the secondary coil.

3. **Substitute the known values into the equation:**
\[ \frac{8000}{8} = \left(\frac{N_1}{N_2}\right)^2 \]

4. **Calculate the left side of the equation:**
\[ \frac{8000}{8} = 1000 \]
So we have:
\[ 1000 = \left(\frac{N_1}{N_2}\right)^2 \]

5. **Take the square root to find the turns ratio:**
\[ \frac{N_1}{N_2} = \sqrt{1000} \]

6. **Calculate the square root:**
\[ \sqrt{1000} \approx 31.62 \]

7. **Round the result to a suitable number:**
The turns ratio can be approximated to:
\[ \frac{N_1}{N_2} \approx 32:1 \]

8. **Conclusion:**
The required turns ratio of the transformer is approximately 32:1.