Question

Find the equivalent resistance between the terminals F and B in the network shown in the figure below given that the resistance of each resistor is 10 ohm.

Answer 1

Applying Kirchhoff’s voltage law to loop FGHF, we get,

– 10I₁ – 10(I₁ – I₂) + 10(I – I₁) + 10(I – I₁) = 0

∴ – 10I₁ – 10I₁+ 10I₂ + 10I – 10I₁ + 10I – 10I₁ = 0

∴ 201 – 40I₁ + 10I₂ = 0 

∴ 2I – 4I₁ + I₂ = 0 …… (1)

Applying Kirchhoff’s voltage law to loop GABHG, we get,

– 10I₂ – 10I₂ + 10(I – I₂) + 10(I₁ – I₂) = 0

∴ – 20I₂ + 10I – 10I₂ + 10I₁ – 10I₂ = 0

∴ 10I + 10I₁ – 40I₂ = 0 .

∴ I + I₁ – 4I₂ = 0 …… (2)

Applying Kirchhoff’s voltage law to loop EFHBCDE, we get,