A cube is soldered together írom identical pieces of wire each of a resistance r. It is connected to the circuit at the corners lying on opposite ends of a body diagonal Find the equivalent resistance.

Answer

`R=r/3+r/6+r/3=(5r)/5`

Explanation

It is clear from considerations of symmetry that the potentials at points 2, 4 and 5 coincide, i.e. `Psi_(2)= Psi_(4)= Psi_(6)=Psi` Hence the potentials at points `delta, delta and 3` coincide as well: `Psi_(5)=Psi_(5)=Psi_(3)=Psi..`. If we short circuit the points at equal potential, i.e. connect the points by means of conductors of negligible resistance, the resistance of the circuit remains unchanged. The circuit obtained in this way is shown in Fig. 26.51. Its resistance is equal to tho sum of the resistances of three series connected sections of three, six, and three parallel connected branches each.