Please show me the final answer :) In the transformer shown in the figure below,

Question

Please show me the final answer :)

In the transformer shown in the figure below, the load resistance RL is 46.0 ?. The turns ratio N1/N2 is 2.30, and the rms source voltage is ?VS = 82.0 V. If a voltmeter across the load resistance measures an rms voltage of 24.0 V, what is the source resistance Rs?
?

In the transformer shown in the figure below, the load resistance RL is 46.0 ?. The turns ratio N1/N2 is 2.30, and the rms source voltage is ?VS = 82.0 V. If a voltmeter across the load resistance measures an rms voltage of 24.0 V, what is the source resistance Rs?

Explanation / Answer

The equivalent resistance is,

           R = [N1/N2]2} (RL)

               = [2.30]2 (46.0 ohms)

               = 243.34 ohms

The voltage across the source coil is,

          V1 = [N1/N2]V2

               = (2.30)(24.0 V)

               = 55.2 V

Thus, the voltage drop is,

             dV = 82.0 V - 55.2 V

                  = 26.8 V

The current through the source is,

         I = V/R + Rs

                 = 82.0 V / 243.34 ohms + Rs

Hence, the source resistance is,

         Rs = dV/I

              = (26.8 V) / [ 82.0 V / 243.34 ohms + Rs]

              = (26.8 V)[ 243.34 ohms + Rs] / 82 V

After solving the above equation, we get

             Rs = 118.143 ohms

                   = 118 ohms

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