Question

A wire with a resistance of 6.0 0 is drawn out through a die so that its new length is three times its original length. Find the resistance of the longer wire, assuming that the resistivity and density of the material are unchanged.

Answer 1

Answer:

Explanation:

initial resistance, R = 6 ohm

initial length, l = l

final length, l' = 3l

Let the initial area of the wire is A and the final area is A'

mass of the wire remains constant

A x l = A' x l'

A x l = A' x 3l

A' = A/3

The formula for the resistance is given by

$R=\rho \frac{l}{A}$   ... (1)

The new resistance is R' which is given by

$R'=\rho \frac{l'}{A'}$

By substituting the values of l' and A', we get

$R'=\rho \frac{3l}{\frac{A}{3}}$

R' = 9 R

R' = 9 x 6 = 54 ohm