Q. A wire of length $5m$ and radius $1\ mm$ has a resistance of $1\ ohm.$ What length of the wire of the same material at the same temperature and of radius $2\ mm$ will also have a resistance of $1\ ohm$
A) $1.25\ m$
B) $2.5\ m$
C) $10\ m$
D) $20\ m$
Explanation
(d) $R \propto \frac{1}{r^{2}} \Rightarrow \frac{R_{1}}{R_{2}} = \frac{l_{1}}{l_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}} \Rightarrow \frac{1}{1} = \frac{5}{l_{2}} \times \left( \frac{2}{1} \right)^{2} \Rightarrow l_{2} = 20m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.