Question

The resistance of a wire is 10 ohm. If it is streached uniformly till it's lenght is doubled, what will be its new resistance?​

Answer 1

Answer:

40 Ω

Explanation:

Continuing from the picture :

$R_{1} = \frac{p(l_{1})^{2}}{V}$

$R_{2} = \frac{p(l_{2})^{2}}{V}$

⇒ $\frac{R_{2}}{R_{1}} = \frac{(l_{2})^{2}}{(l_{1})^{2}}$

Given that R₁ = 10 Ω and l₂ = 2l₁

⇒ R₂ = R₁ × $(\frac{l_{2}}{l_{1}}) ^{2}$

⇒ R₂ = 10 × $(\frac{2l_{1}}{l_{1}} )^{2}$

⇒ R₂ = 10 × 4

∴ R₂ = 40 Ω.

Thanks !