TOPIC 5 ELECTRICITY Because of these three factors, we have the following relationship:
Resistance of a circular conductor R í l __ A
R = resistance (Ω), l = length of conductor (m), A = cross-sectional area of conductor (m2) Resistivity
Given that each conductor has varying resistance based on a number of factors, resistivity is the constant that links resistance with length and cross-sectional area.
Resistivity is scalar and is measured in Ω m.
From this, we now have the constant of proportionality ρ. This is the resistivity of a material and is only constant for a particular material used. Table 24.1 gives examples of different resistivities.
As a material becomes less conductive, its resistivity increases. This means resistance is inversely proportional to conductivity.
Pay particular attention to nichrome and manganin as these tend to be the most common materials used in your resistivity experiments.
Putting all this together gives the formula:
Resistivity ρ = RA
____ l
ρ = resistivity (Ω m), R = resistance (Ω), A = cross-sectional area (m2), l = length (m) QUESTIONS AND ANSWERS
7. A 5 m long copper wire of 0.35 mm diameter has a resistivity of 1.69 × 10–8 Ω m. Calculate its resistance.
Solution ρ = RA
____ l ⇒ 1.69 × 10–8 = R(π(0.175 × 10–3)2)
⇒ (1.69 × 10–8)(5)
___________________ 9.6211 × 10–8 = R ⇒ 0.878 Ω = R
You may now complete Exercise 24C (page 274).
You may now proceed with the mandatory experiment: Measurement of the resistivity of the material of a wire (page 449).
270 FUSION
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8. Calculate the resistivity of an unknown wire when 2 m of 0.45 mm diameter circular wire has a resistance of 7 Ω.
