Question

Two square metal plates $\text{A}$ and $\text{B}$ are of the same thickness and material. The side of $\text{B}$ is twice of that of $\text{A}$. These are connected as shown in figure (series connection). If $R_A$ and $R_B$ are the resistances of $\text{A}$ and $\text{B},$ respectively, then $R_A/R_B$ is

• A. $1:2$
• B. $2:1$
• C. $1:1$
• D. $4:1$

Answer 1

The correct option is C $1:1$

By formula of resistance, we have $$R=\frac{\rho l}{A}$$Here, metal plates $\text{A}$ and $\text{B}$ are of the same material hence, $\rho$ is same for both the plates.

Now, $L_A=l$ and $L_B=2l$
$A_A=A$ and $A_B=2A$

$\frac{R_A}{R_B}=\frac{L_A{A}_B}{L_B{A}_A}$

$\Rightarrow \frac{R_A}{R_B}=\frac{L\times 2A}{2L\times A}$

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

Hence, option (c) is correct answer.