Question

a piece of resistance wire has a resistance of 16 ohm its diameter is doubled now its resistance will be

Answer 1

.R (resistance )= resistivity×length/area of cross section

resistance os inversely proportional to area or d^2/4
so if diameter doubles resistance will become 1/4 of intial value
thats is 4 ohm

Answer 2

The new resistance becomes 4 ohms.

Explanation:

Resistivity of a wire is given by :

$R=\rho \dfrac{l}{A}$............(1)

l is length of wire,

A is area, $A=\pi (d/2)^2$

If the diameter of wire is doubled, $A'=\pi (2d/2)^2=\pi d^2$

New resistance becomes :

$R'=\rho \dfrac{l}{\pi d^2}$.........(2)

Dividing equation (1) and (2) we get :

$\dfrac{R}{R'}=\dfrac{\dfrac{\rho l}{\pi (d/2)^2}}{\dfrac{\rho l}{\pi d^2}}\\\\\dfrac{R}{R'}=4\\\\\dfrac{16}{R'}=4\\\\R'=4\ \Omega$

So, the new resistance becomes 4 ohms.

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