There is an infinite wire grid with cells in the form of equilateral triangles. The resistance of each wire between neighboring joint connections is `R_0` The net resistance of the whole grid between the points A and B as shown in fig.

Options

A. `R_0`
B. `(R_0)/(2)`
C. `(R_0)/(2)`
D. `(R_0)/(3)`

Answer

C

Explanation

We will solve this problem by the superposition principle. Let
current I enter at A, then current `I//6` will flow through AB.
Now, in the second case, let the current be extracted from B,
again current `I//6` will flow through AB. Now, if simultaneously
current enters at A and leaves at B, then the current `I//6 +I//6`
`=I//3` should flow through AB
and current `I - I//3 = 2I//3` will
flow through the remaining
part. Let the resistance fo the
remaining part be `R_1`
Now `(R_0I)/(3) = (R_1 2I)/(3) or R_1 = (R_0)/(2)`
or `R_(eq) =(R_1R_0)/(R_1 +R_0) = ((R_0//2)R_0)/((R_0//2) +R_0) = (R_0)/(3)`