Question

(ntse exam question) A wire of resistance R is stretched to twice of its original length. Its new resistance will be : (1) 4R (2) R/4 (3) 2R (4) R/2

Answer 1

$R= \frac{\rho l}{A} \\ \\ \Rightarrow R= \frac{\rho l}{(V/l)} \\ \\ \Rightarrow R= \frac{\rho}{V} \times l^2 \\ \\ \Rightarrow R\ \alpha\ l^2$

So if length is increased twice, resistance will increase 4 times.
So R' = 4R