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(D) For maximum power transfer,the impedance of the source must match the impedance of the load as seen through the transformer.Let the primary circui

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$\frac{N_1}{N_2}=\sqrt{\frac{Z_1}{Z_2}}$

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(D) For maximum power transfer,the impedance of the source must match the impedance of the load as seen through the transformer.Let the primary circuit have impedance $Z_1$ and the secondary circuit have impedance $Z_2$.The transformer transforms the load impedance $Z_2$ to the primary side as $Z_2' = (N_1/N_2)^2 Z_2$.For maximum power transfer,the primary impedance $Z_1$ must equal the reflected load impedance $Z_2'$.So,$Z_1 = (N_1/N_2)^2 Z_2$.Rearranging this,we get $(N_1/N_2)^2 = Z_1/Z_2$.Taking the square root on both sides,we get $N_1/N_2 = \sqrt{Z_1/Z_2}$.

$A$ transformer may be used to provide maximum power transfer between two $AC$ circuits that have different impedances $Z_1$ and $Z_2$. The ratio of turns $N_1/N_2$ needed to meet this condition is given by :-

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