Conductivity Formula
Electrical conductivity is also the property of conductor. Conductivity is a measure of a material’s ability to conduct an electric current. Electrical conductivity is the reciprocal of electrical resistivity. Conductivity is denoted by sigma (σ).
σ = 1/ρ ——- (1)
σ = 1/RA/L
σ = L/RA —— (2)
The SI unit of conductivity is Siemens/meter (S/m).
Numericals on Conductivity:
(1) What is the resistivity of material?
If the length of wire is 42cm, radius of wire is 0.7 mm and resistance is 20Ω.
Given:
L = 42 cm = 42×10-2m
r = 0.7mm = 0.7×10-3m
7×10-4m
R = 20Ω
1st we calculate the area of wire
A = πr2 = 3.14× (7×10-4)2
= 3.14×14×10-8
= 43.96×10-8
ρ = RA/L
ρ = 20 × (43.96×10-8)/42×10-2
ρ = 20×43.96×10-8/42×10-2
ρ = 879.2/42 × 10-6
ρ = 20.93 × 10-6
ρ = 2.09 × 10-5 Ωm
The resistivity of wire is 2.09×10-5 Ωm.
(2) Calculate the resistance of tungsten wire having length at 1.4km and diameter of 0.3mm.
Given:
Resistivity of tungsten (ρ) = 5.6×10-8 Ωm
L = 1.4 km = 1.4×103m
d = 0.3mm = 0.3×10-3m
A = πr2
∴ A = π × (d/2)2
= π/4 × (0.3×10-3)2
= 3.14/4 × (0.3×10-3)2
A = 3.14/4 × 0.09 × 10-6
= 0.785×0.09×10-6
A = 0.0706×10-6
R = ρ L/A
R = 5.6×10-8×1.4×103/0.0706×10-6
R = 7.84×10-5/0.0706×10-6
R = 111.04×101 Ω
R = 1110.4 Ω
The resistance of tungsten is 1110.4Ω.