This document provides information about electricity and magnetism, specifically resistance and heating effects of currents. It explains that resistance depends on the material and cross-sectional area of a conductor. It also describes Ohm's law, which states that current is directly proportional to voltage in a conductor. Resistors can be made of nichrome wire or ceramic and carbon. Kirchhoff's laws are introduced to help solve circuit problems using conservation of charge and energy.

1. Electricity andElectricity and
MagnetismMagnetism
Topic 5.2 Heating effect ofTopic 5.2 Heating effect of
currentscurrents

2. ResistanceResistance
A tungsten filament lamp has a highA tungsten filament lamp has a high
resistance, but connecting wires have a lowresistance, but connecting wires have a low
resistance.resistance.
What does this mean?What does this mean?
The greater the resistance of a component,The greater the resistance of a component,
the more difficult it is for charge to flowthe more difficult it is for charge to flow
through it.through it.

3. The electrons make many collisions with theThe electrons make many collisions with the
tungsten ions as they move through thetungsten ions as they move through the
filament.filament.
But the electrons move moreBut the electrons move more
easily through the coppereasily through the copper
connecting wires becauseconnecting wires because
they make fewer collisionsthey make fewer collisions
with the copper ions.with the copper ions.

4. Resistance is measured in ohms (Resistance is measured in ohms (ΩΩ) and is defined) and is defined
in the following way:in the following way:
The resistance of a conductor is the ratio of theThe resistance of a conductor is the ratio of the
p.d.p.d. applied across it, to theapplied across it, to the currentcurrent passingpassing
through it.through it.
In fact:In fact:

5. ResistorsResistors
Resistors are components that are made toResistors are components that are made to
have a certain resistance. They can behave a certain resistance. They can be
made of a length of nichrome wire ormade of a length of nichrome wire or
chiseled ceramic and carbon.chiseled ceramic and carbon.

6. Circuit DiagramsCircuit Diagrams
You need to be able to recognize and useYou need to be able to recognize and use
the accepted circuit symbols included in thethe accepted circuit symbols included in the
Physics Data BookletPhysics Data Booklet

7. Ohm’s LawOhm’s Law
The current through a metal wire isThe current through a metal wire is
directly proportional to the p.d. across itdirectly proportional to the p.d. across it
(providing the temperature remains(providing the temperature remains
constant).constant).
This is Ohm's law.This is Ohm's law.
Materials that obey Ohm's law are calledMaterials that obey Ohm's law are called
ohmic conductors.ohmic conductors.

9. When X is aWhen X is a metal resistance wiremetal resistance wire
the graph is a straight line passingthe graph is a straight line passing
through the origin: (if thethrough the origin: (if the
temperature is constant)temperature is constant)
This shows that:This shows that: II is directlyis directly
proportional to V.proportional to V.
If you double the voltage, the currentIf you double the voltage, the current
is doubled and so the value of V/I isis doubled and so the value of V/I is
always the same.always the same.

11. Since resistance R =V/I, the wire hasSince resistance R =V/I, the wire has
a constant resistance.a constant resistance.
The gradient is the resistance on a VThe gradient is the resistance on a V
against I graph, and 1/resistance in aagainst I graph, and 1/resistance in a
I against V graph.I against V graph.

12. For a filament lamp, doubling theFor a filament lamp, doubling the
voltage produces less than double thevoltage produces less than double the
current.current.
This means that the value of V/I risesThis means that the value of V/I rises
as the current increases.as the current increases.
As the current increases, the metalAs the current increases, the metal
filament gets hotter and the resistancefilament gets hotter and the resistance
of the lamp rises.of the lamp rises.

14. Resistance of wireResistance of wire
Resistance through a solid depends onResistance through a solid depends on
1)1)LengthLength
2)2)Cross-sectional AreaCross-sectional Area
3)3)Material (ie free electrons and atomicMaterial (ie free electrons and atomic
diameter)diameter)
R = ρ l/A

15. ResistivityResistivity
Data table from physnet.co.ukData table from physnet.co.uk
Calculate resistance ofCalculate resistance of
a)a)2m of copper of 0.5mm2m of copper of 0.5mm
diameterdiameter
b)b)50cm of graphite, 25050cm of graphite, 250μμm inm in
diameterdiameter
c)c)1.7mm of aluminium, 201.7mm of aluminium, 20μμmm
in diameterin diameter

16. Power DissipationPower Dissipation

17. Power DissipationPower Dissipation

18. Resistance CombinationsResistance Combinations

19. Resistors in seriesResistors in series

20. The diagram shows three resistors connected inThe diagram shows three resistors connected in
series.series. There are 3 facts that you should know forThere are 3 facts that you should know for
a series circuit:a series circuit:
1.1. the current through each resistor in series isthe current through each resistor in series is
the samethe same
2.2. the total p.d., V across the resistors is thethe total p.d., V across the resistors is the
sum of the p.d.s across the separatesum of the p.d.s across the separate
resistors, so: V = Vresistors, so: V = Vll + V+ V22 + V+ V33
3.3. the combined resistance R in the circuit isthe combined resistance R in the circuit is
the sum of the separate resistors,the sum of the separate resistors,
R = RR = Rll + R+ R22 + R+ R33

21. Suppose we replace the 3 resistors withSuppose we replace the 3 resistors with
one resistor R that will take the sameone resistor R that will take the same
current I when the same p.d. V is placedcurrent I when the same p.d. V is placed
across it.across it.

22. This is shown in the diagram. Let's calculateThis is shown in the diagram. Let's calculate
R. We know that for the resistors in series:R. We know that for the resistors in series:
V = VV = Vll + V+ V22 + V+ V33
But for any resistor: p.d. = current xBut for any resistor: p.d. = current x
resistance (V = I R).resistance (V = I R).
If we apply this to each of our resistors, andIf we apply this to each of our resistors, and
remember that the current through eachremember that the current through each
resistor is the same and equal to I, we get:resistor is the same and equal to I, we get:
IR = IRIR = IRll+IR+IR22+IR+IR33
If we now divide each term in the equationIf we now divide each term in the equation
by I, we get:by I, we get:
R = RR = R11 + R+ R22 + R+ R33

23. Resistors in parallelResistors in parallel

24. We now have three resistors connected inWe now have three resistors connected in
parallel.parallel. There are 3 facts that you should knowThere are 3 facts that you should know
for a parallel circuit:for a parallel circuit:
1.1. the p.d. across each resistor in parallel isthe p.d. across each resistor in parallel is
the samethe same
2.2. the current in the main circuit is the sum ofthe current in the main circuit is the sum of
the currents in each of the parallelthe currents in each of the parallel
branches, so:branches, so:
I = II = I11 + I+ I22 + I+ I33
3. the combine3. the combined resistanced resistance RR is calculated from theis calculated from the
equation:equation:

25. Suppose we replace the 3 resistors with oneSuppose we replace the 3 resistors with one
resistorresistor RR that takes the same total current Ithat takes the same total current I
when the same p.d. V is placed across it.when the same p.d. V is placed across it.

26. This is shown in the diagram. Now let'sThis is shown in the diagram. Now let's
calculatecalculate R.R.
We know that for the resistors inWe know that for the resistors in
parallel:parallel:
I = II = I11+I+I22+I+I33
But for any resistor, current = p.d. =But for any resistor, current = p.d. =
resistanceresistance (I = V/R ).(I = V/R ). If we apply this toIf we apply this to
each of our resistors, and remembereach of our resistors, and remember
that the p.d. across each resistor is thethat the p.d. across each resistor is the
same and equal to V,same and equal to V,

27. we get:we get:
V/V/R=V/RR=V/R11 + V/R+ V/R22 + V/R+ V/R33
Now we divide each term by V, to get:Now we divide each term by V, to get:
1/1/R=1/RR=1/R11 + 1/R+ 1/R22 + 1/R+ 1/R33
You will find that the total resistanceYou will find that the total resistance R isR is alwaysalways
less than the smallest resistance in the parallelless than the smallest resistance in the parallel
combination.combination.

28. Ammeters and VoltmetersAmmeters and Voltmeters
In order to measure the current, an ammeter isIn order to measure the current, an ammeter is
placedplaced in series,in series, inin the circuit.the circuit.
What effect might this have on the size of theWhat effect might this have on the size of the
current?current?
TheThe idealideal ammeter hasammeter has zerozero resistance, so thatresistance, so that
placing it in the circuit does not make the currentplacing it in the circuit does not make the current
smaller.smaller.
Real ammeters do have very small resistances ‑Real ammeters do have very small resistances ‑
around 0.01around 0.01 ΩΩ..

29. A voltmeter is connectedA voltmeter is connected in parallelin parallel with awith a
component, in order to measure the p.d. acrosscomponent, in order to measure the p.d. across
it. Why can this increase the current in theit. Why can this increase the current in the
circuit?circuit?
Since the voltmeter is in parallel with theSince the voltmeter is in parallel with the
component, theircomponent, their combinedcombined resistance is lessresistance is less
than the component's resistance.than the component's resistance.
TheThe idealideal voltmeter hasvoltmeter has infiniteinfinite resistance andresistance and
takes no current.takes no current.
Digital voltmeters have very high resistances,Digital voltmeters have very high resistances,
around 10 Maround 10 MΩΩ, and so they have little effect on, and so they have little effect on
the circuit they are placed in.the circuit they are placed in.

30. Potential dividersPotential dividers
A potential divider is a device or a circuitA potential divider is a device or a circuit
that uses two (or more) resistors or athat uses two (or more) resistors or a
variable resistor (potentiometer) to provide avariable resistor (potentiometer) to provide a
fraction of the available voltage (p.d.) fromfraction of the available voltage (p.d.) from
the supply.the supply.

31. The p.d. from the supply is divided acrossThe p.d. from the supply is divided across
the resistors in direct proportion to theirthe resistors in direct proportion to their
individual resistances.individual resistances.

32. Take the fixed resistance circuit - this is aTake the fixed resistance circuit - this is a
seriesseries circuit therefore the current in thecircuit therefore the current in the
same at all points.same at all points.
IIsupplysupply = I= I11 = I= I22
Where IWhere I11 = current through R= current through R11
II22 = current through R= current through R22

33. Using Ohm’s LawUsing Ohm’s Law

34. ExampleExample

35. With sensorsWith sensors
A thermistor is a device which will usuallyA thermistor is a device which will usually
decrease in resistance with increasingdecrease in resistance with increasing
temperature.temperature.
A light dependent resistor, LDR, willA light dependent resistor, LDR, will
decrease in resistance with increasing lightdecrease in resistance with increasing light
intensity. (intensity. (LLightight DDecreases itsecreases its RResistance).esistance).

36. ExampleExample
Calculate the readings on the meters shownCalculate the readings on the meters shown
below when the thermistor has a resistancebelow when the thermistor has a resistance
ofof
a) 1 ka) 1 kW (W (warm conditions) and b) 16 kwarm conditions) and b) 16 kW.W.
((cold conditionscold conditions))

38. Kirchoff’s lawKirchoff’s law
Solving electric circuit problems involvesSolving electric circuit problems involves
finding current and voltage values for everyfinding current and voltage values for every
component in the circuit. There are rulescomponent in the circuit. There are rules
that can assist you in these calculations.that can assist you in these calculations.
AA junctionjunction is a point where 3 or more wiresis a point where 3 or more wires
connect, aconnect, a looploop is all the wire andis all the wire and
componenets in a circle and acomponenets in a circle and a branchbranch is allis all
the wires and components connecting onethe wires and components connecting one
junction to another.junction to another.

39. 1.1. Assign current labels to each branch. AAssign current labels to each branch. A
current entering a junction is positive, onecurrent entering a junction is positive, one
leaving is negative. From theleaving is negative. From the
conservation of charge you get theconservation of charge you get the sumsum
of currents to a junction is zero.of currents to a junction is zero. ApplyApply
this rule to each junction to obtain a set ofthis rule to each junction to obtain a set of
equations.equations.

40. 2. Give each resistor a voltage and each cell2. Give each resistor a voltage and each cell
an emf. Sum of all the energy in each loopan emf. Sum of all the energy in each loop
should be zero from the conservation ofshould be zero from the conservation of
energy, so theenergy, so the sum of pd = zerosum of pd = zero..