Question

given wire of resistance 1 ohm is streched to double its lenght what will be its new resistance

Answer 1

R = ρL / A
R = ρL^2 / V

When wire is stretched Volume (V) remains constant.

∴ R ∝ L^2

From above relation if length (L) is doubled resistance (R) will quadruple.

Hence, new resistance will be 4Ω

Answer 2

Answer:

Given : l₁ = l ;  R₁ = 1 ; l₂ = 2l ; R₂ = ?

volume of wire will be same in both cases so,

                                    A₁l₁ = A₂l₂

                                    l₁÷ l₂ = A₂÷ A₁                            ... (i)

we know that,            R₁ = ρ* l₁ / l₂                                ... (ii)

                                                               

                                   R₂ = ρ * l₂ / A₂                            ... (iii)

Now dividing equations  (ii) by (iii)

                                   R₁/R₂ = l₁ / l₂ · A₂/A₁

                                            = ( l₁/l₂)² = (l / 2l )²

                                   R₁/R₂ = 1/4

                                      R₂ = 4R₁ = 4 × 1

                                      R₂ = 4 Ω