For the network shown in the figure, Y₁₁ and Y₁₂ are, respectively

Concept:

Y parameters are also known as short circuit parameters.

In Y parameters input and output currents are represented in terms of input and output voltages.

I₁ = Y₁₁.V₁ + Y₁₂.V₂

I₂ = Y₂₁.V₁ + Y₂₂.V₂

Calculation:

To calculate Y₁₁,

Short-Circuiting the output voltage V₂ 

Applying KVL in input loop we get,

V₁ = 10I₁ + 5(I₁ + I₂) ----- (1)

Now apply KVL in output loop we get,

4I₂ – 8I₁ + 5(I₁ + I₂) = 0

\({I_2} = \frac{{{I_1}}}{3}\)----(2)

Putting value of I₂ from equation (2) to equation (1) to get value of Y₁₁

\({V_1} = 15{I_1} + \frac{{5{I_1}}}{3}\)

\(\frac{{{I_1}}}{{{V_1}}}|{V_{2 = 0}} = {Y_{11}} = \frac{3}{{50}}mho\)

Now short-circuiting the input voltage V₁ to calculate Y₁₂,

Applying KVL in input loop,

10I₁ + 5(I₁ + I₂) = 0

I₂ = -I₁------ (3)

Now apply KVL in outer loop,

V₂ = 4I₂ – 8I₁ + 5(I₁ + I₂)

V₂ = 9I₂ – 3I₁------ (4)

Putting value of I₂ from equation (3) to equation (4) we get

V₂ =  – 30I₁

\(\frac{{{I_1}}}{{{V_2}}}|{V_{1 = 0}} = {Y_{12}} = - \frac{1}{{30}}mho\)