Question

Fig shows an infinite wire grid with infinite cells. The resistance of each wire in the cell is $R_0$. Find the resistance $R_{AB}$ of the whole grid between the terminals A and B ?

Answer 1

If $V$ is the voltage applied across AB then $V=IR=I_0{R}_0$ where $R$ is the resistance of segment AB. The symmertric condtions yeild $\frac{I}{4}$ where $i$ is the current flowing through all the four segments meeting at B. Thus $\frac{I}{2}$ current flows through conductor AB. , that is $I_0=\frac{i}{2}$or $R=\frac{R_0}{2}$