Question

A Piece of wire of resistance 29 ohm is drawn out so that its length increased to twice its original length. calculate the resistance of the wire in the new situation.

Answer 1

$R= \frac{pl}{A}=29$
when l'=2l
A'=A/2
so $R'= \frac{pl'}{A'}=4 \frac{pl}{A}=4(29)=116$
so new resitance is 116 ohm

Answer 2

R = pl/A

p=density , l=length , A = area

Multiplying l to both numerator and denominator,

R = pl^2 / V

V = Volume

R proportional to l^2

So when l is doubled , R becomes 4 times.

So R=116 ohm