Question

In an infinite grid of square cells made of conducting wires, resistance of an edge of a square cell is R. In the figure, point C is midpoint of the edge AB. Find resistance of the entire grid as measured between the terminal pairs A-C.

• A. R
• B. $\frac{R}{2}$
• C. $\frac{3R}{8}$
• D. 2R

Answer 1

Answer: (C)

$\frac{3R}{8}$

Answer 2

The problem asks for the equivalent resistance between a vertex A and the midpoint C of an adjacent edge AB in an infinite square grid of resistors, where each edge has resistance R. This is a standard problem in the analysis of infinite resistor networks. The resistance between a vertex and the midpoint of an adjacent edge with resistance R in an infinite square grid is a known result, which is $\frac{3R}{8}$. Applying this result directly, the resistance between A and C is $\frac{3R}{8}$.