Question

A wire of resistance 2 ohmis stretched to double its length.what is the new resistance of the wire?what is the change in resistivity?

Answer 1

Answer:

Resistance= Resistivity x length/area

When the wire is stretched to double the length , the area of cross section gets reduced to half.

So

New Resistance = Resistivity x 2length/area/2

New resistance = (Resistivity x area/length)x4

i.e, New resistance = Resistance x 4

So in this case resistance 2 Ohms will change to 2X4 =8 ohms

note: length of the wire is doubled, its area of cross-section is halved so as to keep the volume of the wire constant.

there wont be any change in resistivity .resistivity independent of the dimensions of the sample.

Explanation:

Answer 2

original resistance of wire, R1 = 2 ohm

new resistance of wire be R2

original length of the wire be L1

new length of the wire be L2

original area of crossection of the wire be A1

new area of crossection of the wire be A2

rho is the resistivity of the wire

R1/R2 = (rho L1/A1)/(rho L2/A2)

as volume of the wire remains same = A1L1  = A2L2 = V

multiplying and dividing RHS Numerator with L1 and denominator with L2

R1/R2 = (rho L1^2/A1L1)/(rho L2^2/A2L2)

R1/R2 = (L1^2/ V)/(L2^2/ V)

R1/R2 = (L1^2)/(L2^2)

as L2 = 2 L1

R1/R2 = (L1^2)/((2L1)^2)

R1/R2 = 1/4

R2 = 4 R1

R2 = 4 x 2

R2 = 8 ohm

Resistivity of the wire does not change because it only dependes on the nature of the material of conductor.