Answer to Question #91797 in Electric Circuits for Jahnavi

Question

If an iron wire is drawn to decrease it's radius by 0.5 precent of increase in its resistance will be

Answer 1

The resistance of a wire of length $l$ and cross-sectional area $A$ is given by

$$R=\rho \frac{l}{A}$$

where $\rho$ is the resistivity of the material of the wire.

If radius is decreased by 0.5 % then new radius $r'=0.995r$

New area $A'=\pi r'^2=(0.995)^2\pi r^2 = (0.995)^2A$

New resistance $R'=\rho \frac{l}{(0.995)^2A}=\frac{R}{0.995^2}=1.01R$

Percentage increase in resistance

$$=\frac{R'-R}{R}\times 100\\ =\frac{1.01R-R}{R}\times 100\\ =1$$

Increase in resistance = 1 %