Question

Figure shows two squares, $X$ 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 across the length $L$. What is the value of $R_x/R_y$?

• A. 1/4
• B. 1/2
• C. 1
• D. 2

Answer 1

The correct option is C 1

The resistance of the square $X$ is given by

$R_x=\rho \frac{L}{Lt}=\frac{\rho }{t}$

where $\rho$ is the resistivity on the metal. Similarly,

$R_y=\rho \frac{2L}{\left(2L\right)t}=\frac{\rho }{t}$

same as before. Hence, $R_x/R_y=1$