N1 Engineering Science|The Easy Way! 133 Summary 6.3


Grouping of resistors Resistors in series


• RT = R1 + R2 + R3 ohms • Current is common (the same) i.e. IT = I1 = I2 = I3 Resistors in parallel • 1


RT = 1 + 1 R1 R2 + 1 R3


NB: Do not forget to invert 1


RT in the second last step.


• The pd is the same across each branch (VT = V1 = V2 = V3) Resistivity


• Four factors influence the resistance of a conductor; – type ofmaterial [resistivity (ρ)], – length (ℓ), – cross-sectional area (A), and – temperature (t).


• R = ρℓ A ohms ... (as long as the temperature remains constant)


R = resistance in ohms (Ω), ρ = resistivity in ohm metres (Ωm) NB: for micro-ohm metres (µΩm) ... remember × 10–6, A = cross-sectional area in m2 ... mm2 = × 10–6 m2


Definition of resistivity Resistivity is the resisting power of a specified material. • A good conductor has a low resistivity. • A poor conductor has a high resistivity. • R ∝ ℓ – similar to resistors in series.


• R ∝ 1 A – similar to resistors in parallel. Temperature coefficient of resistance


• The resistance ofmostmaterials are affected by changes in temperature. • Good conductors: resistance increases with an increase in temperature – positive temperature coefficient of resistance.


• Insulators: resistance decreases with an increase in temperature – negative temperature coefficient of resistance.


Definition of temperature coefficient of resistance Temperature coefficient of resistance is the increase in unit resistance of a substance, per unit rise in temperature from 0 °C.


• Rt = Ro (1 + αot) ohms t = temperature in °C


Rt = resistance at a temperature t °C Ro = resistance at a temperature of 0 °C αo = temperature coefficient of resistance at 0 °C


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