Question

A wire of resistance 4 Ohm is streched to double its length calclulate its new resistance​

Answer 1

Answer:

If a wire is stretched to double its length, what will its new resistance be? When the wire is stretched to double the length , the area of cross section gets reduced to half. So when the wire is stretched, the resistance multiplies by four times

Answer 2

Answer:

Given : l₁ = l ;  R₁ = 4 ; 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 = 4/4

                                      4R₂ = 4R₁ = 4 × 4

                                      R₂ = 16 Ω