Q. Equal amounts of a metal are converted into cylindrical wire of different lengths $L$ and cross-sectional area $A.$The wire with the maximum resistance is the one, which has
A) Length=$L\ and\ area = A$
B) $lengths = \frac{L}{2}\ and\ area = 2A$
C) $lengths = 2L\ and\ area = \frac{A}{2}$
D) All have the same resistance, as the amount of the metal is the same
Explanation
(c) Resistance, $R = \rho\frac{l}{A}$
$R \propto l \propto \frac{1}{A}$
∴R is maximum when
$length = 2L\ and\ area = \frac{A}{2}.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.