Question

Find the equivalent resistance between the terminals of A 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 in loop ABHGA,

−IR2 - (I − I₂)R + (I − I₁)R + R(I − I₁)

∴ −I₁R − I₁R + I₂R + 2IR − 2I₁R = 0

∴ −4I₁R + I₂R + 2IR = 0

⇒ 4I₁ − I₂ = 2I               ...(i)

Applying Kirchhoff's voltage law in loop GHKFG,

∴ −I₂R − I₂R + (I − I₂)R + R(I₁ − I₂) = 0

∴ − 2I₂R + IR − I₂R + I₁R − I₁R = 0

∴ − 4 I₂R + IR + I₁R = 0

⇒ 4I₂ − I − I₁ = 0

∴ 4I₂ − I₁ = I                ...(ii)

Applying LVL in loop EDCBFE,

−(I − I₁)R − (I − I₁)R − (I − I₂)R + E = 0

∴ 2(I − I₁)R + (I − I₂)R = E              ...(iii)

∴ I₁ = `3/5"I"`   and   I₂ = `2/5"I"`

∴ `7/5`IR = E      ...[from equation (3)]

∴ `7/5`IR = IR¹

∴ R¹ = `7/5`R 

= `7/5`R

= `7/5xx10`

= 14 Ω