Question

Two square metal plates A and B are of the same thickness and material. The side of B is twice that of A. If the resistances of A and B are denoted by $R_A$ and $R_B$, Then $\left(\frac{R_A}{R_B}\right)$ is

• A. $\frac{1}{2}$
• B. $2$
• C. $1$
• D. $4$

Answer 1

The correct option is C $1$

The resistance is given by
$R=\frac{\rho L}{A}$
here, metal plates A and B are of the same material hence, $\rho$ is same for both the plates.
Now, $L_A=l$ and $L_B=2l$
As thickness t, of both the plates is same
$\Rightarrow A_A=2l^2+2lt+2lt$
$\therefore A_A=2l^2+4lt$
$\therefore A_A=2l(l+2b)$
and similarly $A_B=4l(l+2b)$
Now,
$\frac{R_A}{R_B}=\frac{L_A{A}_B}{L_B{A}_A}$

$\frac{R_A}{R_B}=\frac{l\times 4l(l+2b)}{2l\times 2l(l+2b)}$

$\frac{R_A}{R_B}=1$