Question

a wire of resistance 10 ohms is uniformly streched till lenght becomes 3 times. find resistance of strecthed wire​

Answer 1

Given :

A wire of resistance 10Ω is uniformly stretched till length becomes 3 times.

To Find :

New resistance of stretched wire.

Solution :

Let original length of wire be L and area of cross section be A.

Now it is uniformly stretched till length becomes 3 times. Here volume of wire remains constant$.$

➙ Initial V = Final V

➙ A₁L₁ = A₂L₂

• L₁ = L and L₂ = 3L

➙ A₁L = 3A₂L

➙ A₂ / A₁ = 1 / 3

We know that resistance of conductor is directly proportional to the length of conductor and inversely proportional to the area of cross section.

• R ∝ L / A

➛ R₁ / R₂ = (L₁ / L₂) × (A₂ / A₁)

➛ 10/R₂ = (L/3L) × (1/3)

➛ 10/R₂ = 1/9

➛ R₂ = 10 × 9

➛ R₂ = 90 Ω

∴ New resistance of stretched wire will be 90Ω.