Question

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

• A. $R_0$
• B. $\frac{R_0}{2}$
• C. $\frac{R_0}{3}$
• D. $\frac{R_0}{4}$

Answer 1

Answer: (C)

$\frac{R_0}{3}$

Here net resistance between points A and B is to be found. Let, I be the current enters at A and exit from B.

When I enters at A then by symmetry current $\frac{I}{6}$ will flow in branch AB from A to B. Also, current $\frac{I}{6}$ must flow through branch AB before leaving point B.

Superimposing this two the current $(\frac{I}{6}+\frac{I}{6})$ will flow through branch AB.

Hence net resistance $R_{eq}$ is

$R_{eq}=(\frac{I}{6}+\frac{I}{6})R_0$

$R_{eq}=2\left(\frac{I}{6}\right)R_0$

$\therefore R_{eq}=\frac{R_0}{3}$