Question

A wire of length 5$m$ 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$m$

Answer 1

Answer: (D)

20$m$

Answer 2

$R \propto \frac{l}{r^{2}}$⇒ $\frac{R_{1}}{R_{2}} = \frac{l_{1}}{l_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}} \Rightarrow \frac{1}{1} = \frac{5}{l_{2}} \times \left( \frac{2}{1} \right)^{2} \Rightarrow l_{2} = 20m$