Transformers and phasors question please?
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The maximum power transfer to the load occurs when the load impedance matches the source impedance. The load impedance is obvious &mdash; 100&Omega; &mdash; but the source impedance is R2 in series with whatever impedance the combination of I1, R1 and XFMR1 represent.

Impedances in series simply add, so the total source impedance connected to the load is the effective impedance at the right side of XFMR1, plus R2. Therefore, we need the impedance of XFMR1 to be RN - R2 = 100&Omega; - 75&Omega; = 25&Omega;.

The actual source impedance of I1 and R1 together is just R1, or 1&Omega;. Therefore, we need the transformer to convert 1&Omega; on the left to 25&Omega; on the right. A transformer converts impedances in proportion to the square of its turns ratio n, so we need to know what value of n will create a 1:25 transformation:

$$n^2 = \frac{25\Omega}{1\Omega}$$

$$n = \sqrt{25} = 5$$