Suppose that you wish to fabricate a uniform wire out of 1 gram of copper.If the wire is to have a resistance of R=0.5Ω,and all of the copper is to be used.What will be(i)the length and (ii)the diameter of the wire.


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Question Number 41443 by Necxx last updated on 07/Aug/18

$S u p p o s e t h a t y o u w i s h t o f a b r i c a t e$ $a u n i f o r m w i r e o u t o f 1 g r a m o f$ $c o p p e r . I f t h e w i r e i s t o h a v e a$ $r e s i s t a n c e o f R = 0.5 Ω, a n d a l l o f$ $t h e c o p p e r i s t o b e u s e d . W h a t w i l l$ $b e (i) t h e l e n g t h a n d (i i) t h e d i a m e t e r$ $o f t h e w i r e .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 07/Aug/18

	$m = Π r^{2} l d r = r a d i u s o f w i r e$ $l = l e n g t h o f w i r e$ $d = d e n s i t y o f w i r e$ $ρ = r e s i s t i v i t y o f w i r e$ $R = r e s i s t a n c e o f w i r e$ $m = m a s s o f w i r e$ $R = \frac{ρ l}{Π r^{2}}$ $m . R = d . ρ . l^{2}$ $l = \sqrt{\frac{m . R}{d . ρ}}$ $r^{2} = \frac{m}{Π l d}$ $r^{2} = \frac{m}{Π d .} \times \sqrt{\frac{d . ρ}{m . R}} = \frac{1}{Π} . \sqrt{\frac{m . ρ}{d . R}}$ $r = \frac{1}{\sqrt{Π}} \times {(\frac{m . ρ}{d . R})}^{\frac{1}{4}}$ $d i a = \frac{2}{\sqrt{Π}} \times {(\frac{m . ρ}{d . R})}^{\frac{1}{4}}$
	Commented by Necxx last updated on 07/Aug/18

	$y e a h . . . . T h a n k s$
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