If a transformer of an audio amplifier has output impedance $8000 \Omega$ and the speaker has input…

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
  1. $1000: 1$
  2. $100: 1$
  3. $1: 32$
  4. $32: 1$

Solution

$\begin{aligned} & \frac{\mathrm{Z}_1}{\mathrm{Z}_2}=\left(\frac{\mathrm{N}_1}{\mathrm{~N}_2}\right)^2 \\ & \frac{8000}{8}=\left(\frac{\mathrm{N}_1}{\mathrm{~N}_2}\right)^2 \\ \therefore \quad & \frac{\mathrm{~N}_1}{\mathrm{~N}_2}=\frac{10 \sqrt{10}}{1} \approx \frac{32}{1}\end{aligned}$

Asked in: MHT CET 2024 (16 May Shift 2)

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