Question 320: 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: