Question

Resistance of a wire is yΩ. The wire is stretched to triple its length, then the resistance becomes

Answer 1

➡ Given:

✏ initial length = L

✏ final length = 3L

✏ initial resistance = y $\Omega$

➡ Calculation:

$\implies \rm \: R_2 = {n}^{2} R_1 \\ \\ \therefore \rm \: R_2 = {3}^{2} y \\ \\ \therefore \underline{ \boxed{ \bold{ \rm{ \orange{R_2 = 9y \: \Omega}}}}}$

Answer 2

Given: Resistance - R = yΩ

            original lenght = L

             new length = 3L

To Find: New Resistance = R' =?

Solution:

Formula used:

• R = ρl/A , where ρ = Resistivity, l = length of the wire, A = cross-sectional area of wire

Solution:

• According to the above formula, the length is directly proportional to Resistance.
• The wire is just stretched, so the cross-sectional area will remain the same as well as the resistivity as it is a quantity depending on the nature of the substance, the wire is made of.

R = ρL/A

R' = ρ3L/A

R' = 3R

and R = y (given)

Hence, R' = 3y

Therefore, on stretching the wire to triple its length,  the resistance becomes 3y.