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(D) The impedance matching condition for a transformer is given by the relation: $\frac{Z_p}{Z_s} = \left(\frac{N_p}{N_s}\right)^2$. Given: Primary im

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$32: 1$

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(D) The impedance matching condition for a transformer is given by the relation: $\frac{Z_p}{Z_s} = \left(\frac{N_p}{N_s}ight)^2$. Given: Primary impedance $Z_p = 8000 \ \Omega$ and secondary impedance $Z_s = 8 \ \Omega$. Substituting the values: $\frac{8000}{8} = \left(\frac{N_p}{N_s}ight)^2$. $1000 = \left(\frac{N_p}{N_s}ight)^2$. Taking the square root on both sides: $\frac{N_p}{N_s} = \sqrt{1000} = 10\sqrt{10}$. Since $\sqrt{10} \approx 3.16$,we get $\frac{N_p}{N_s} \approx 10 	imes 3.16 = 31.6 \approx 32$. Therefore,the ratio of primary to secondary turns is $32: 1$.

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

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