Resistivity

Other than temperature, resistance also depends on
  • Length, L
  • Cross-sectional area, A or thickness of wire
  • Type of material (resistivity, ρ)

Note 
  • The cross-section of a wire is a circle.
  • Resistivity ρ is a property of the material. It is a constant. The lower the resistivity, the better the conductor of electricity.

R = ρL⁄A

where R = resistance (in Ω)
           ρ = resistivity (in Ωm)
           L = length (in m)
           A = cross-sectional area (in m2)

R is directly proportional to its length and resistivity;
R is inversely proportional to its cross-sectional area.
Example:

(a) Determine the resistance of the wire X.
(b) The length of the wire X is doubled and its cross-sectional area halved. Determine the new resistance and hence ammeter reading.
(c) Given that the diameter of the 50 cm long wire is 5 mm, determine its resistivity.
Answer:
(a) R = V/I = 3.0/0.15 = 20 Ω
(b) L doubled -> R doubled
A halved -> R doubled
new R = 20 * 4 = 80 Ω
I = V/R = 3.0/80 = 0.0375 A

(c) A = pi*(0.005/2)2 = 1.96*10-5 m2
R = pL⁄A
20 = p*0.5⁄1.96*10-5
p = 7.85*10-4 Ωm
Excel@Physics