Two plates R and S of the same material are in the form of a square and have the same thickness. A side of S is twice the side of R. Compare their resistances. The direction of current is shown by an arrow head.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Both have the same resistance
The resistance of a conductor is \( R=\rho l/A \), where \( l \) is the length along the current and \( A \) the cross-section across it.
From the figure, the current flows parallel to one side of each square plate.
So for a plate of side \( a \) and thickness \( t \), the length is \( a \) and the cross-section is \( a\times t \).
\( \begin{aligned} R_{\mathrm{R}} &= \frac{\rho\,a}{a\,t} \\ &= \frac{\rho}{t} \end{aligned} \)
\( \begin{aligned} R_{\mathrm{S}} &= \frac{\rho\,(2a)}{(2a)\,t} \\ &= \frac{\rho}{t} \end{aligned} \)
From the above, \( R_{\mathrm{R}}=R_{\mathrm{S}} \). Hence the resistance of a square plate depends only on its material and thickness. The size of the side does not matter, so both plates have the same resistance.