Question

The following table gives the lengths of three copper rods and their diameters. The resistances between the two ends of the rods arranged in ascending order is

Rod	Length	Diameter
A	$l$	d
B	$2l$	$d/2$
C	$l/2$	d
D	$l$	$d/2$

• A. A, B, C, D
• B. C, A, B, D
• C. C, A, D, B
• D. C, B, D, A

Answer 1

Answer: (C)

C, A, D, B

$R_A=\frac{\rho l}{\frac{\pi d^2}{4}}=\frac{4\rho l}{\pi d^2}$

$R_B=\frac{\rho 2l}{\frac{\pi d^2}{16}}=\frac{32\rho l}{\pi d^2}$

$R_C=\frac{\rho l}{\frac{2\pi d^2}{4}}=\frac{2\rho l}{\pi d^2}$

$R_D=\frac{\rho l}{\frac{\pi d^2}{16}}=\frac{16\rho l}{\pi d^2}$

$\Rightarrow Increasingorder{R}_C,R_A,R_D,R_B$