What are the lattice equivalent network parameters ZA and ZB of a symmetrical π network shown in the figure?

Z₁₁ = Z₂₂= \(\frac{Z_B+ Z_A}{2}\)

Z₁₂ = Z₂₁ = \(\frac{Z_B- Z_A}{2}\)

\(\pi \rightarrow T network\)

R₁ = 10 Ω

R₂ = 5 Ω

R₃ = 10 Ω

R1 = \(\frac{10\times 5}{10+5+10} = \frac{50}{25} = 2\Omega\)

R2 = \(\frac{10\times5}{25}= 2\Omega\)

R3 = \(\frac{10\times10}{25}=\frac{100}{25} = 4\Omega\)

Z₁₁ = 2 + 4 = 6 Ω

Z₁₂ = Z21 = 4 Ω

Z₂₂ = 2 + 4 = 6 Ω

Z₁₁ = Z₂₂ = \(\frac{Z_B+ Z_A}{2}\)

6 = \(\frac{Z_B+ Z_A}{2}\)

⇒ Z_B + Z_A = 12      ......................(1)

4 = \(\frac{Z_B- Z_A}{2}\) 

⇒ ZB -ZA = 8          ........................(2)

Solving equation (1) & (2), we get

Z_B = 10 Ω

Z_A  = 2 Ω

Here, option 1 is correct.