Answer to Question #91795 in Electric Circuits for Jahnavi

Question

A wire resistance 18 ohm is drawn until it's radius reduce 1\2 of its original radius then resistance of the wire is

Answer 1

$R_{1}$ = 18 ohm

Relation to resistivity and conductivity: $R_{1}=\rho\frac{l}{S_{1}}$

$r_{2}=\frac{1}{2}r_{1}$ , $S_{1}=\pi {r_{1}^2}$

and $S_{2}=\pi {r_{2}^2} = \frac{1}{4}{S_1}=\frac{1}{4}{\frac{\rho{l}}{R_{1}}}$

Then $R_{2}=\rho\frac{l}{S_{2}} = \frac{4{R_{1}{\rho}l}}{{\rho}l}=4R_{1}=72 ohm$