Question

A wire of length L and cross section area a is streched to twice of its length such that volume remaind constant. Find new resistance

Answer 1

It is known that,

$R=\frac{\rho l}{A}$

$l^{\prime }\to 2l$

$\therefore C^{\prime }{A}^{\prime }$has to be changed

Now, volume=$\frac{Mass}{Density}$

and volume is maintened to be constant

also, volume=legth$\times$ cross-sectional area

$\therefore$ if $l^{\prime }\to 2l$

$\therefore A^{\prime }=\frac{A}{2}$

Thus, ressitance will increse $4$ times due to doubling the length of wire.