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Electric Current 3Resistance

- Unit 1.3a3
- Breithaupt chapter 4.3
- pages 50 to 52

AS specification

- Resistance is defined by R V / I
- Ohms law.
- ? RA / L
- Superconductivity as a property of certain

materials which have zero resistivity at and

below a critical temperature which depends on the

material. Applications (e.g. very strong

electromagnets, power cables). - Breithaupt chapter 4.3 pages 50 to 52

Resistance

- resistance p.d. across a component

current through the component - R V / I
- also V I R and I V / R
- resistance in measured in ohms (O)
- potential difference in volts (V)
- electric current in amperes (A)
- Resistance is a measure of the difficulty of

making a current pass through a substance. It is

caused by the repeated collisions between the

charge carriers and the positive ions of the

substance. - Resistance simulation at Phet Resistance

equation demo at Phet

Questions

- 1. Calculate the resistance of a device if a

current of 250mA flows when a potential

difference of 6V is applied - R V / I
- 6V / 0.250A
- 24 O
- 2. Calculate the current that flows through a

resistance of 4MO when 60V is applied across it - I V / R
- 60 V / 4 000 000 O
- 0.000 015 A 15 µA

Complete

Answers

Measuring resistance

- Set up the circuit opposite.
- Measure the current through the resistor with the

ammeter. - Measure the potential difference across the

resistor with the voltmeter. - Calculate resistance using R V / I .
- Further sets of values of I and V can be obtained

by changing the setting of the variable resistor.

From these an average value for resistance can be

obtained. - Note The resistance of the voltmeter should be

as high as possible so that the ammeter only

measures the current through the resistor. - Fendt Ohms law simulation

Ohms law

- Ohms law states that the potential difference

across an ohmic conductor is proportional to the

current through it, provided the physical

conditions do not change. - A graph of p.d. against current for a conductor

obeying ohms law will be a straight line through

the origin. - The gradient of such a graph is equal to the

resistance of the conductor. - Physical conditions remaining constant include

temperature and the dimensions of the conductor

Resistivity (?)

- Experiments show the the resistance of a

conductor is - 1. proportional to its length, L
- 2. inversely proportional to its

cross-section area, A - and so R a L /A
- the constant of proportionality is the

resistivity, ? of the conductor - Therefore R ? L A
- Reisistivity equation demo at Phet
- KT resistivity simulation

Variation in resistivity

- Resistivity is measured in ohm-metre, Om.
- Metals (e.g. copper) and other good conductors

have very low resistivities. - Good insulators (e.g. PVC) have very high

resistivities. - Semiconductors (e.g. silicon) have intermediate

resistivities - Resistivity table on Wikipedia

Superconductivity

- Superconductivity is a state where certain

materials have zero resistivity. - This occurs at and below a critical temperature

(Tc) which depends on the material. Tc is usually

below 200oC. - Applications include
- very strong electromagnets (e.g. in MRI scanners)
- power cables to prevent wastage of electrical

energy (e.g. to supply the LHC)

Questions on resistivity

- 1. Calculate the resistance of a 0.30m length of

copper wire of cross-section area 5 x 10-6 m2

resistivity of copper 1.7 x 10-8 Om - R ? L A
- (1.7 x 10-8 Om) x (0.30m) / (5 x 10-6 mm2)
- 0.00102 O 1.02 mO
- 2. Repeat the above question, this time with

silicon resistivity of silicon 2300 Om - (2300 Om) x (0.30m) / (5 x 10-6 mm2)
- 1.38 x 106 O 138 MO

3. Calculate the resistivity of a metal wire of

cross-section diameter 0.4mm if a 25cm length of

this wire has a resistance of 6O.

- A pd2
- 4
- p x (4 x 10-4 m)2 / 4
- p x (1.6 x 10-7 m2) / 4
- cross-section area 1.2566 x 10-7 m2
- ? RA
- L
- (6 O) x (1.2566 x 10 -7 m2 ) / (0.25 m)
- resistivity 3.02 x 10 -6 Om

Notes from Breithaupt pages 50 to 52

- What is resistance? Give the equation defining

resistance and a sample resistance calculation. - Draw a circuit diagram and explain how resistance

can be measured. - What is Ohms law? How can Ohms law be verified

graphically? - Give the equation for resistivity. Calculate the

resistance of a copper wire of diameter 1mm and

length 3m. - Compare the resistivities of copper, silicon and

PVC. - What is superconductivity? When does it occur?

Give two applications. - Try the summary questions on page 52

Answers to the summary questions

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