The figure below shows an $AC$ source, a transformer with a turns ratio of $\frac{N_1}{N_2}=2\mathrm{.}70,$ a source resistor $R_S,$ and a load resistor $R_{L-}$

A voltmeter across the load resistor measures an rms voltage of $26\mathrm{.}0$ V when the load resistor $R_L$ is $43\mathrm{.}0$ and the rms source voltage is $V_S=81\mathrm{.}0V.$

$($a$)$ Determine the value of the source resistor $R_s($in $).$

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$($b$)$ What If$?$ If the turns ratio is increased to $3\mathrm{.}00,$ determine the source resistance $($in $)$ required to deliver the same amount of power to the load.

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