Two square shaped metal plates of A and B of same thickness ( $t$ ) and of same material are connected as…
Two square shaped metal plates of A and B of same thickness ( $t$ ) and of same material are connected as shown in the figure. The side of $B$ is twice that of $A$. If the resistance of $A$ and $B$ are $R_A$ and $R_B$ respectively then $\frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}$ is
$\frac{1}{2}$
2
1
4
Solution
$\mathrm{L}_{\mathrm{A}}=\mathrm{L}$ and $\mathrm{L}_{\mathrm{B}}=2 \mathrm{~L}$ then $A_A=A$ and $A_B=2 A$ By the formula of resistance
$\begin{aligned} & R=\frac{\rho L}{A} \\ & \frac{R_A}{R_B}=\frac{L_A A_B}{L_B A_A}=\frac{L}{2 L} \times \frac{2 A}{A}=1\end{aligned}$
