Question

A wire of resistance 4 ???? is stretched to twice its original
length. The resistance of stretched wire would be [2013]
(a) 4 ???? (b) 8 ????
(c) 16 ???? (d) 2 ????

Answer 1

Answer:

Resistance is a measure of the opposition that a circuit (or an electrical element) offers to the flow of electric current . You might compare it to the diameter of a hose. In fact, for metal wire, this is an excellent analogy: small-diameter wire has high resistance (a lot of opposition to current flow), and large-diameter wire has low resistance (not much opposition to electric currents). Resistance is measured in Ohms, Ω.

The dependence of resistance on length L and area of cross-section A of a wire is,

R = ρL/A

a)Resistance ‘R’ is related to length of the wire ‘L’, area of cross-section of the wire ‘A’ and resistivity ‘ρ’ as,

formula==> R = ρL/A

When Length is doubled

new length L'=2L

and area of cross-section is halved

new area of cross-section A'=A/2

then the new resistance is,

R ' = ρL'/A' = ρ(2L)/(A/2)=4ρL/A

=> R' = 4R

Thus, the resistance increases by 4 times.

change in resistance = resistance of the wire after stretching-resistance of the wire before stretching

=R'-R =4R-R

=3R

b)resistivity do not change on stretching it is a property of the material it remains constant for a particular material.it do not depend on length and area of conductor