Question

The resistance of a 1 m long nichrome wire is 6 Ω. If we reduce the length of the wire to 70 cm. what will its resistance be?

Answer 1

Resistance of a wire is directly proportional to its length. Let R₁ and R₂ be the resistances of the nichrome wire at 100 cm (1 m) and 70 cm, respectively.

We know R= ρ(L/A)

∴ R₁= ρ (L₁/A) .....(i)   and R₂ =ρ (L₂/A) .....(ii)

Dividing (ii) by (i), we get

R₂/R₁ = L₂/L₁ = 70/100

⇒ R₂ = (70/100) × R₁

Now, R₁ = 6 Ω

⇒R₂=(70/100)×6 = 0.7 x 6

= 4.2 Ω
Required Resistance = 4.2 Ω