GATE 2015 EE – Question 56

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 2 marks · Numerical answer

In a linear two-port network, when 10 V is applied to Port 1, a current of 4 A flows through Port 2 when it is short-circuited. When 5 V is applied to Port 1, a current of 1.25 A flows through a $1\ \Omega$ resistance connected across Port 2. When 3 V is applied to Port 1, the current (in Ampere) through a $2\ \Omega$ resistance connected across Port 2 is ________.

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Correct answer: 0.4 to 0.6

Explanation

Write the current out of Port 2 as $I = g_{21}V_1 - g_{22}V_2$. The short-circuit test gives $g_{21} = \frac{4}{10} = 0.4$. With 5 V at Port 1 and a $1\ \Omega$ load, $V_2 = 1.25$ V and $I = 1.25$, so $1.25 = 2 - 1.25\,g_{22}$ and $g_{22} = 0.6$. With 3 V and a $2\ \Omega$ load, $V_2 = 2I$, so $I = 1.2 - 1.2I$, which gives $I = \frac{1.2}{2.2} = 0.545$ A.