The transmission parameter matrix [T] for an ideal transformer with a turns ratio of n1 : n2 is given by

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ESE Electronics 2012 Paper 1: Official Paper
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  1. \(\left[ \begin{matrix} \frac{n_1}{n_2} & 1 \\ 0 & \frac{n_2}{n_1} \\ \end{matrix} \right]\)
  2. \(\left[ \begin{matrix} \frac{n_1}{n_2} & 0 \\ 0 & \frac{n_2}{n_1} \\ \end{matrix} \right]\)
  3. \(\left[ \begin{matrix} \frac{n_1}{n_2} & 1 \\ 0 & -\frac{n_2}{n_1} \\ \end{matrix} \right]\)
  4. \(\left[ \begin{matrix} \frac{n_1}{n_2} & 0 \\ 1 & -\frac{n_2}{n_1} \\ \end{matrix} \right]\)

Answer (Detailed Solution Below)

Option 2 : \(\left[ \begin{matrix} \frac{n_1}{n_2} & 0 \\ 0 & \frac{n_2}{n_1} \\ \end{matrix} \right]\)
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Detailed Solution

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The transmission parameters are given as:

V1 = AV2 - BI2

I1 = CV2 -DI2

F2 Neha 24.11.20 Pallavi D5

The voltage equations for an ideal transformer are as follows:

\(V_1=\frac{n_1}{n_2} V_2\)

\(I_2 = -\frac{n_2}{n_1} I_1\)

The transmission parameter matrix is given by:

\(\left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{I_1}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} n_1/n_2&0\\ 0&n_2/n_1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{V_2}}\\ { - {I_2}} \end{array}} \right]\)

∴ Option 2 is correct

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