Equivalent π network The currents I1 and I2 at the output

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Equivalent π network The currents I₁ and I₂ at the output of 2-port network can be written as
I₁ = 5V₁ – V₂
I₂ = – V₁ + V₂
Which one of the following gives the parameters of an equivalent π network shown above?

1. y₁ = 4Ω, y₂ = 0, y₃ = 1Ω
2. y₁ = 4Ω, y₂ = 4, y₃ = 1Ω
3. y₁ = 1Ω, y₂ = 1Ω, y₃ = 1Ω
4. y₁ = 4Ω, y₂ = 0, y₃ = 2Ω

Correct Option: A

The Y-parameter are represented by expressions:
I₁ = Y₁₁V₁ + Y₁₂V₂ . . . …(i)
I₂ = Y₂₁V₁ + Y₂₂V₂ . . . …(ii)
The given network:

The given equation
I₁ = 5V₁ – V₂ . . . …(iii)
I₂ = – V₁ + V₂ . . . …(iv)
On comparing equation (i) and (ii) with (iii) and (iv), we get:
y₁₁ = 5, y₁₂ = – 1
y₂₁ = – 1, y₂₂ = 1
For a π-network
y₁₁ = y₁ + y₃ = 5
y₂₂ = y₂ + y₃ = 1
y₁₂ = y₂₁ = – y₃ = – 1, i.e., y₃ = 1Ω
So,
y₁ = 5 – y₃ = 5 – 1 = 4Ω
and
y₂ = 1 – y₃ = 1 – 1 = 0Ω
Hence alternative (A) is the correct choice.