Question
Consider a thin square sheet of side $$L$$ and thickness $$t,$$ made of a material of resistivity $$\rho .$$ The resistance between two opposite faces, shown by the shaded areas in the figure is
Consider a thin square sheet of side $$L$$ and thickness $$t,$$ made of a material of resistivity $$\rho .$$ The resistance between two opposite faces, shown by the shaded areas in the figure is
A.
directly proportional to $$L$$
B.
directly proportional to $$t$$
C.
independent of $$L$$
D.
independent of $$t$$
Answer :
independent of $$L$$
Solution :
We know that $$R = \rho \frac{l}{a}$$
Where $$l$$ is the length of the conductor through which the current flows and a is the area of cross section.
$$\eqalign{ & {\text{Here}}\,l = L\,{\text{and}}\,a = L \times t \cr & \therefore R = \frac{{\rho L}}{{L \times t}} = \frac{\rho }{t} \cr} $$
$$\therefore $$ $$R$$ is independent of $$L$$
We know that $$R = \rho \frac{l}{a}$$
Where $$l$$ is the length of the conductor through which the current flows and a is the area of cross section.
$$\eqalign{ & {\text{Here}}\,l = L\,{\text{and}}\,a = L \times t \cr & \therefore R = \frac{{\rho L}}{{L \times t}} = \frac{\rho }{t} \cr} $$
$$\therefore $$ $$R$$ is independent of $$L$$
