Twelve wires each having resistance 2 Ω are joined to form a cube. A battery of 6 V emf is joined across point a and c. The voltage difference between e and f i $s ______$ V.

Question

Twelve wires each having resistance 2 Ω are joined to form a cube. A battery of 6 V emf is joined across point a and c. The voltage difference between e and f i s ______ V.

G1 Physics · Accepted Answer

Image Using symmetry, current through branches e-b and g-d is zero. Equivalent resistance of the cube between a and c is: Rₑq = 3R/4 For R = 2 Ω: Rₑq = 3/2 Ω Battery current: I = 6/(3/2) = 4 A By symmetry, the relevant branch current is: i₂ = 1 A Potential difference between e and f: ΔV = (i₂/2)R = (1/2) × 2 = 1 V