A wire of resistance R 1 R₁ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is:

Step-by-step solution

As per the given question, the change in the length is ∆ l = 2 l . Resistance of a wire is given by, R = ρ l A Therefore, R 1 = ρ l 1   A 1 When the length is starched by 2 l 1 , final length will be l 2 = l 1 + 2 l 1 = 3 l 1 . As the volume remains constant l 2 A 2 = l 1 A 1     ⇒ A 2 = A 1 3 . Therefore, R 2 = ρ 3 l 1   A 1 3 = 9 ρ l 1   A 1 ∴ R 2 R 1 = 9