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Resistivity

Resistivity. Electricity Lesson 5. Learning Objectives. To define resistivity . To know what causes resistance. To know how to measure resistance. Practice Conversion. If a wire has a cross sectional area of 1.23 square millimetres What is its area in square metres.

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Resistivity

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  1. Resistivity Electricity Lesson 5

  2. Learning Objectives To define resistivity. To know what causes resistance. To know how to measure resistance.

  3. Practice Conversion If a wire has a cross sectional area of 1.23 square millimetres What is its area in square metres.

  4. What does resistance depend on? The resistance of a wire depends on three factors: the length; double the length, the resistance doubles. the area; double the area, the resistance halves. the material that the wire is made of.

  5. Resistivity For a conductor of length L and uniform cross-sectional area, A, its resistance R is proportional to L but inversely proportional to A. So the resistance is given by:- Where ρ is the resistivity of the conductor.

  6. Resistivity Rearranging gives an equation for resistivity:- The unit of resistivity is the ohm metre (Ωm) In words:-

  7. Resistivity Resistivity is a property of the material.  It is defined as the resistance of a wire of the material of unit area and unit length. It has the symbol ρ, don’t mix this up with density!

  8. Cross Sectional Area For a circular conductor with a radius r, diameter d, the cross sectional area is given by:-

  9. Question Constantan has a resistivity of 47 × 10-8Ωm.  How much of this wire is needed to make a 10 ohm resistor, if the diameter is 0.5 mm? 

  10. Answer  Work out the radius in metres:  r  = 0.25 × 10-3 m  Now work out the area:  A = πr2 = π × (0.25 × 10-3)2 =  π × 6.25 × 10-8 m2= 1.96 × 10-7 m2  Now work out R: R = ρL/A . 10 = (47 × 10-8 Wm × L ) / 1.96 × 10-7 m2   L = 10 × 1.96 × 10-7 m2 ¸ 47 × 10-8 =  4.17 m 

  11. Superconductivity • Normally materials have some resistance. • When current flows through them they heat up. • But superconductors can be cooled below a transition temperature below which the resistivity disappears. • This means no energy is lost as heat energy. • For metals the transition temp is about 10 K • (-263 °C)

  12. Uses of superconductors... Power cables that can transmit electricity with no loss of energy. Really strong electromagnets that don’t need a constant power source (e.g. Maglev trains). Electronic circuits that work really fast.

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