Figure 5.260 shows two square, X and Y cut from a sheet of metal of uniform thickness t. X and Y have sides of length L and 2L, respectively.

The resistances `R_x and R_y` of the squares are measured between the opposite faces shaded in fig. What is the value of `R_x//R_y?`

Options

A. `1//4`
B. `1//2`
C. 1
D. 2

Answer

C

Explanation

The resistance of the square X is given by
`R_(x) = rho(L)/(Lt) = (rho)/(t)`
where `rho` is the resistivity on the metal. Similarly,
`R_Y = rho(2L)/((2L)t) =(rho)/(t)`
same as before. Hence, `R_x//R_Y = 1`