Derive the expression for resistance of wire having cross-sectional area A and length l and Deduce ohm's law? How resistivity of material depends on factors for metal and alloy explain ?
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Answer:
(a) Define resistivity. Write an expression for the resistivity of a substance. Give the meaning of each symbol which occurs in it.
(b) State the SI unit of resistivity.
(c) Distinguish between resistance and resistivity.
(d) Name two factors on which the resistivity of a substance depends and two factors on which it does not depend.
(e) The resistance of a metal wire of length 1m is 26Ω at 20
∘
C. If the diameter of the wire is 0.3mm, what will be the resistivity of the metal at that temperature ?
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Answer
(a) Resistivity , ρ=
l
R×A
where, R is the resistance of the conductor
A is the area of cross - section of the conductor
l is the length of the conductor.
(b) Ohm - meter
(c)
1. Resistance is the property of the conductor , while resistivity is the property of the material of the conductor.
2. Resistance of a conductor is the opposition to the flow of electric current through it. Resistivity of a substance is the opposition to the flow of electric current by a rod of that substance which is 1 m long and 1m
2
in cross section.
3. Resistance of a conductor depends on length, thickness , nature of material and temperature of the conductor ; while resistivity of a substance depends on the nature of the substance and temperature.
(d) Resistivity of a substance depends on the nature of the substance and its temperature. It does not depend on the length or thickness of the conductor.
(e) l=1m
R=26ohm
r=
2
d
=
2
0.3
mm=0.15mm=0.15×10
−3
m
ρ=
l
R×A
=
l
R×πr
2
=
1
26×3.14×(0.15×10
−3
)
2
=1.83×10
−6
Ωm