Q. The following four wires are made of the same material and are at the same temperature. Which one of them has highest electrical resistance?
A) Length =50 cm, diameter=0.5 mm
B) Length =100 cm, diameter=1 mm
C) Length=200 cm , diameter=2 mm
D) Length=300cm, diameter=3 mm
Explanation
(a) The resistance of a conductor
$\therefore R = \rho\frac{1}{\pi r^{2}}$
$\Longrightarrow \ \ R \propto \frac{1}{r^{2}}$
$(a)R_{1} = \frac{50}{\left( 0.25 \times 10^{- 1} \right)^{2}} = 800 \times 10^{2}\Omega$
$(b)R_{2} = \frac{100}{\left( 0.5 \times 10^{- 1} \right)^{2}} = 400 \times 10^{2}\Omega$
$(c)R_{3} = \frac{200}{\left( 1 \times 10^{- 1} \right)^{2}} = 200 \times 10^{2}\Omega$
$(d)R_{4} = \frac{300}{\left( 1.5 \times 10^{- 1} \right)^{2}} = 133.3 \times 10^{2}\Omega$
Hence, electrical resistance of first wire is maximum.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.