Question

Twelve equal wires each of resistance 'r' are joined to form a cube. Find the resistance between two corners on the same edge of the cube

Answer 1

Answer:

Suppose a potential difference V is applied between the points a and c so that a current I enters at a and the same current leaves at c. The current distribution is shown in figure.ltbygtBy symmetry, the paths ad and ab are equivalent and hence will carry the same current

i1. Thepathahwillcqrrythesamecurrent

(using Kirchhoff's junction law).Similarly at junction c, currents coming form dc and bc will be

i1

each and fron fc will be

i - 2i1

Kirchhoff's junction law at b and d shows that currents through be and dg will be zero and hence may be ignored for further analysis. Omitting these two wires, the circuit is redrawn in figure. <br> The wire hef and hgf are joined in parallel and have equivalent resistance

(2r) (2r) / (2r) + (2r) = r

between h and f.This is jioned in series with ah and fc giving equivalent resistance

r + r + r = 3r

This 3r is jioned in parallel with adc (2r)and abc(2r) between a and c, <br> the equivalent resostance R between a and c is, therefore, given by <br>

1/R = 1/3r + 1/2r + 1/2r

giv ∈ gR = 3/4 r