Question 303: AC fundamentals

Question

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

Accepted Answer

The turns ratio of a transformer is given by the square root of the impedance ratio. The impedance ratio is the ratio of the primary impedance to the secondary impedance. For this problem, the primary impedance is $8000 \, \Omega$ and the secondary impedance is $8 \, \Omega$. To find the turns ratio, use the following formula:
$$ 	ext{Turns Ratio} = \sqrt{\frac{Z_{	ext{primary}}}{Z_{	ext{secondary}}}} $$
Substituting the given values:
$$ 	ext{Turns Ratio} = \sqrt{\frac{8000}{8}} $$
$$ 	ext{Turns Ratio} = \sqrt{1000} $$
$$ 	ext{Turns Ratio} = 10 	imes \sqrt{10} $$
To simplify, we find that:
$$ 10 	imes \sqrt{10} \approx 31.62 $$
This value is approximately 32. Therefore, the closest option for the turns ratio is $32: 1$. Thus, the correct answer is:
Option D
$32: 1$

Answer

$1000: 1$

Answer

$100: 1$

Answer

$1: 32$

Answer

$32: 1$

AC fundamentals

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

Choose the correct answer: