Question

A given wire of resistance 1 Ω is stretched to double its length. What will be its new resistance?

Answer 1

Let ‘I’ be the length and ‘a’ be the area of cross – section
of the resistor with resistance, R = 1Ω

`"R" =  ∝ l/r^2`

when the wire is stretched to double its length,
the new length I’ = 2I and the new area of cross section,

`a^1 = a/2  "and"  l^1 = 2l`

`"R"^1 ∝ l^1/a^1`

∴ `"R"^1 ∝ (2l)/(a/2)`

`"R"^1 ∝ (4l)/a`

R¹ ∝ 4R

Resistance increases to 4 times original resistance = R¹ = 4Ω