The resistance of a wire is 5 Ω . Its new resistance in ohm, if stretched to 5 times of its original length will be :

Step-by-step solution

The resistance of a wire ( R ) is related to its resistivity ρ , length ( l ) and cross-sectional area A as: R = ρ l A As the length of wire increases, the cross-sectional area decreases. The cross-sectional area in terms of volume ( V ) and length ( l ) is A = V l ∴   R = ρ l 2 V Taking the volume of wire constant, R ∝ l 2 So if R ' is the resistance of wire after getting redrawn and R is the initial resistance of wire, ∴   R ' R = ( 5 l ) 2 l 2 = 25 ⇒ R &#3