Question 643: Current Electricity

Question

A wire of resistance 4 $\Omega $ is stretched to twice its original length. The resistance of stretched wire would be

Accepted Answer

Resistance of a wire,
$R = ho {l \over A} = 4\Omega $   ...(i)
When wire is stretched twice, its new length be $l'$. Then
$l' = 2l$
On stretching volume of the wire remains constant.
$ 	herefore lA = l'A'$ where A' is the new cross-sectional area
$ \Rightarrow A' = {l \over {l'}}A = {l \over {2l}}A = {A \over 2}$
$ 	herefore $ Resistance of the stretched wire is
$R' = ho {{l'} \over {A'}} = ho {{2l} \over {\left( {A/2} ight)}} = 4ho {l \over A}$
$ = 4\left( {4\Omega } ight) = 16\Omega $

Answer

8 $\Omega $

Answer

16 $\Omega $

Answer

2 $\Omega $

Answer

4 $\Omega $

Current Electricity

A wire of resistance 4 \Omega is stretched to twice its original length. The resistance of stretched wire would be

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