Question 395: Current Electricity

Question

A uniform wire of length 1 and radius r has a resistance of 100 $\Omega $. It is recast into a wire of radius ${r  \over 2}.$  The resistance of new wire will be :

Accepted Answer

Resistance of a wire of length l and radius r is given
by
R = ${{ho l} \over A}$ = ${{ho l} \over A} 	imes {A \over A} = {{ho V} \over {{A^2}}} = {{ho V} \over {{\pi ^2}{r^4}}}$
$ \Rightarrow $ R $ \propto $ ${1 \over {{r^4}}}$
$ 	herefore $ ${{{R_1}} \over {{R_2}}} = {\left( {{{{r_2}} \over {{r_1}}}} ight)^4}$
Given, R
1
= 100 $\Omega $, r
1
= r, r
2
= ${r \over 2}$
, R
2
= ?
$ 	herefore $ R
2
= R
1
${\left( {{{{r_1}} \over {{r_2}}}} ight)^4}$ = 16R
1
= 1600 $\Omega $

Answer

1600 $\Omega $

Answer

400 $\Omega $

Answer

200 $\Omega $

Answer

100 $\Omega $

Current Electricity

A uniform wire of length 1 and radius r has a resistance of 100 \Omega . It is recast into a wire of radius {r \over 2}. The resistance of new wire will be :

Choose the correct answer: