Question

How will the resistance of a wire be affected if its

1. length is doubled, and
2. radius is also doubled ?

Give justification for your answer.

Answer 1

R `=(rho"l")/"A"`

Where, `rho` = electrical resistivity

l = length of the conductor

A = cross-sectional area of the conductor

Hence if the length is double then 

⇒ `"R"_1=rho((2"l"))/"A"`

`therefore   "R"_1 = 2("R")`

So, if the length of the resistance gets doubled then resistance also gets doubled.

Now when the radius is double then

⇒  `"R"_2 = (rho"l")/"A"`

⇒`"R"_2 = (rhol)/(pi(2"r")^2`

`therefore   "R"_2 = 1/4("R")`

So if the radius gets doubled then resistance will be `(1/4)^"th"` of initial resistance.