Question

The resistance of a 20 cm long wire is 5 ohms stretched to a uniform wire of length 40 cm. What is the resistance of the wire?

Answer 1

Resistance of wire will be `"20 Ω"`

Explanation:

Resistance of a wire is given by the formula

`R = (ρl)/A`

`R = (ρl)/A= (ρl)/A × (l/l) = (ρl^2) / (Al) = (ρl^2)/V`

From above relation, `R ∝ l^2` [∵ Resistivity (ρ) and Volume (V) of wire will be same even after stretching].

`R_2/R_1 = (l_2 / l_1)^2`

`R_2 = R_1 × (l_2 / l_1)^2`

`R_2 = "5 Ω" × (("40" cancel"cm") / ("20" cancel"cm"))^2`

`R_2 = "20 Ω"`