A battery of 10 V and negligible internal resistance is connected across the diagonally opposite cor

Question

A battery of 10 V and negligible internal resistance is connected across the diagonally opposite corners of a cubical network consisting of 12 resistors each of resistance $1 \Omega$. Determine the equivalent resistance of the network.

Professor PC Thomas Classes · Answer

By symmetry and Kirchhoff's loop rule, the equivalent resistance of a cube across diagonally opposite corners is $R_{eq} = (5/6)R$. Since $R = 1 \Omega$, $R_{eq} = 5/6 \Omega$.