Question

How does the resistance of a wire change when:; (i) its length is tripled?; (ii) its diameter is tripled?; (iii) its material is changed to one whose resistivity is three times?

Answer 1

Answer:

it's diameter is tripled

Answer 2

Answer:

(1) 3 times

(ii) one-ninth times

(iii) 3 times

Explanation:

The resistance of a wire can be given by

$R\ =\ \rho\dfrac{l}{A}$

where, l = length of the wire

           A = area of cross section of wire

         $\rho\=\ =\ \textrm{resistivity of the wire}$

(1) when its length is tripled

$R_1\ =\ \rho\dfrac{3l}{A}$

              $=\ 3R_1$

Hence, the resistance will be also 3 times.

(2) when its diameter is tripled

$R_2\ =\ \rho\dfrac{l}{\pi(\dfrac{d}{2})^2}$

               $=\ \rho\dfrac{l}{\pi(\dfrac{3d}{2})^2}$

               $=\ \rho\dfrac{l}{9\pi(\dfrac{d}{2})^2}$

               $=\ \dfrac{R}{9}$

Hence, the resistance will become one-ninth times.

(3) when  material is changed to one whose resistivity is three times

$R_3\ =\ 3\rho\dfrac{l}{A}$

               = 3R

hence the resistance will become 3 times.