Question

If a transformer of an amplifier has output impedance \(8000\ \Omega\) and the speaker has input impedance of \(8\ \Omega\), the primary and secondary turns of this transformer connected between the output of amplifier and to loudspeaker should have the ratio

• A. \(1000:1\)
• B. \(100:1\)
• C. \(1:32\)
• D. \(32:1\)

Hint:

The impedance reflected across a transformer changes with the square of the turns ratio.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
A transformer used for impedance matching connects a source of high output impedance to a load of low impedance.
The impedances are related to the turns ratio by
\(\dfrac{Z_p}{Z_s}=\left(\dfrac{N_p}{N_s}\right)^{2}\)

Step 2: Substitute the Values
Here \(Z_p=8000\ \Omega\) and \(Z_s=8\ \Omega\).
\(\dfrac{Z_p}{Z_s}=\dfrac{8000}{8}=1000\)

Step 3: Calculation
\(\dfrac{N_p}{N_s}=\sqrt{1000}\approx 31.6\approx 32\)

Step 4: Compare the options
The ratio of primary to secondary turns is nearly \(32:1\), which matches option (D).

Final Answer:
The primary to secondary turns ratio is about 32 to 1. \[ \boxed{\text{(D) }32:1} \]