Question

Two square plates A and B have same thickness \( t \), material. B’s side is twice A’s. Find \( \frac{R_A}{R_B} \):

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

Hint:

Resistance varies inversely with area. Square shape means \( A \propto l^2 \).

Answer 1

The Correct Option is C

Resistance: \( R = \rho \frac{l}{A} \), for square plate side \( l \), area = \( l^2 \), length = thickness \( t \)
\[ R = \rho \frac{t}{l^2} \quad \Rightarrow R_A = \rho \frac{t}{l^2}, \quad R_B = \rho \frac{t}{(2l)^2} = \rho \frac{t}{4l^2}
\Rightarrow \frac{R_A}{R_B} = \frac{1}{1/4} = 4 \text{ (But length of B is doubled so } \frac{t}{4} \text{ in denominator)}, \Rightarrow R_A = R_B \]