Question

How does the resistance of a wire change when its radius is tripled its material is changed to one whose resistivity is three times?

• A. Resistance increases 3 times
• B. Resistance decreases 3 times
• C. Resistance will be 9times
• D. Resistance will be 2 times

Answer 1

Answer: (B)

Resistance decreases 3 times

Resistance of the wire $R=\rho \frac{L}{\pi r^2}$ $⟹R\propto \frac{\rho }{r^2}$

Given : ${\rho }^{\prime }=3\rho$ $r^{\prime }=3r$

$\therefore$ $\frac{R^{\prime }}{R}=\frac{{\rho }^{\prime }}{\rho }\frac{r^2}{(r^{\prime }{)}^2}=\frac{3}{3^2}=\frac{1}{3}$

Thus resistance of the wire will decrease by 3 times.