Question

A wire have resistance of 10 ohm.A second wire of same material is having length double and radius of cross section half that of the wire .The resistance of second wire is

Answer 1

Answer:

80 ohm

Explanation:

R = specific resistance × length /area of cross section

Answer 2

The resistance of the second wire is 40 ohms.

Explanation:

Resistance of the wire is 10 ohms. The resistance of a wire is given by :

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

$\rho$ = resistivity of wire

If length is doubled, l = 2l and r' = r/2. New resistance becomes :

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

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

$\dfrac{R}{R'}=\dfrac{\dfrac{\rho l}{A}}{\dfrac{\rho (2l)}{\pi (r/2)^2}}\\\\\dfrac{R}{R'}=\dfrac{\dfrac{\rho l}{\pi r^2}}{\dfrac{\rho (2l)}{\pi (r/2)^2}}\\\\\dfrac{R}{R'}=\dfrac{1}{4}\\\\R'=4R\\\\R'=40\ \Omega$

So, the resistance of the second wire is 40 ohms.

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