The resistance of the wire is R 1 . It is now stretched (keeping the volume constant) without breaking so that its length becomes three times. Now the resistance becomes R 2 , then what is the value of R 2 : R 1?

Step-by-step solution

For a given wire, its resistance R ∝ l A ∴ R 1 ∝ l 1 r 1 2 The wire is stretched such that l 2 = 3 l 1 But density is unchanged. ∴ Density = M V = M 4 π r 1 2 l 1 = M 4 π r 2 2 l 2 ⇒ r 2 2 = l 1 r 1 2 l 2 = r 1 2 3 … . . ( i ) ∵ l 2 = 3 l 1 Now, R 2 ∝ l 2 r 2 2 ∴ R 2 ∝ 9 l 1 r 1 2 . . . . ii From ( i ) and ( ii ) ∴ R 2 : R 1 = 9 : 1