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Electricity and magnetism

IGCSE Physics 0625 · Unit 4 revision notes

Magnets and fields, charge, current, p.d. and resistance, circuits and safety, then induction, motors, generators and transformers.

55 definitions to learn word for word, 21 equations in their own column, 33 diagrams and graphs. Read it, cover it, test yourself.

  1. 4.1 Simple phenomena of magnetism
  2. 4.2a Electric charge
  3. 4.2b Electric current
  4. 4.2c Electromotive force and potential difference
  5. 4.2d Resistance
  6. 4.2e Electrical energy and electrical power
  7. 4.3a Circuit diagrams and circuit components
  8. 4.3b Series and parallel circuits
  9. 4.3c Action and use of circuit components
  10. 4.4 Electrical safety
  11. 4.5a Electromagnetic induction
  12. 4.5b The a.c. generator
  13. 4.5c Magnetic effect of a current
  14. 4.5d Force on a current-carrying conductor
  15. 4.5e The d.c. motor
  16. 4.5f The transformer
Definitions (mark-scheme wording)EquationsExam trapsExtended = Extended tier only

4.1Simple phenomena of magnetism

Definitions

Magnetic field
a region in which a magnetic pole experiences a force.
Direction of a magnetic field
the direction of the force on the north pole of a magnet at that point.
Magnetic material
a material attracted by a magnet: iron, steel, nickel and cobalt.
Non-magnetic material
a material that is not attracted by a magnet and cannot be magnetised, e.g. copper, aluminium, plastic.
Induced magnetism
magnetism produced in a magnetic material when it is placed in a magnetic field.
Temporary magnet
a magnet (e.g. soft iron) that loses its magnetism when removed from the field.
Permanent magnet
a magnet (e.g. steel) that keeps its magnetism.

Key points

  • Like poles repel, unlike poles attract; magnetic forces act without contact.
  • A magnet attracts unmagnetised magnetic materials by inducing an opposite pole in the near end.
  • Soft iron magnetises and demagnetises easily: electromagnet and transformer cores, relays.
  • Steel is hard to magnetise but keeps it: permanent magnets (fridge doors, loudspeakers, compasses).
  • Field lines run N to S outside the magnet and never cross.
  • Plot a field with a plotting compass (mark the needle direction dot to dot) or iron filings.
  • Electromagnets can be switched off and their strength varied: scrapyard cranes, relays, door locks.
  • Extended magnetic forces are due to interactions between magnetic fields.
  • Extended the field is strongest where the lines are closest together (at the poles).
NS closest lines= strongest field
Bar magnet field: lines leave N and enter S; crowded lines near the poles mean a stronger field.
NS NS attract NS SN repel NS NS attract soft iron (induced poles)
Attraction, repulsion and induced magnetism: a magnet induces an opposite pole in the near end of soft iron.

Watch out!

  • Attraction proves nothing: a magnet attracts any iron. Only repulsion proves an object is a magnet.
  • Field lines go from N to S outside the magnet; arrows the wrong way lose the mark.

4.2aElectric charge

Definitions

Conductor
a material that allows charge (electrons) to flow through it easily, e.g. metals.
Insulator
a material that does not allow charge to flow through it easily, e.g. plastic, rubber, glass.
Coulomb (C)
Extended the unit of electric charge.
Electric field
Extended a region in which an electric charge experiences a force.
Direction of an electric field
Extended the direction of the force on a positive charge at that point.

Key points

  • There are two kinds of charge, positive and negative. Like charges repel, unlike charges attract.
  • Charging by friction transfers electrons only: the object gaining electrons becomes negative, the one losing them positive.
  • Detect charge: a charged rod hung on a thread is repelled by a like-charged rod.
  • Test a conductor: put it in a circuit with a cell and lamp; the lamp lights only if it conducts.
  • Metals conduct because they contain free (delocalised) electrons; insulators have none.
  • Extended field lines point away from positive and towards negative; radial round a point charge or charged conducting sphere, uniform between parallel plates.
− − − − − − + + + + rod: negative cloth: positive electrons move only electrons move, never positive charge
Charging by friction: electrons rub off the cloth onto the polythene rod. Rod negative, cloth positive.
+ point charge +− uniform field
Extended: field lines point away from + and towards -; radial round a point charge, uniform between plates.

Watch out!

  • Never say positive charge moves when charging by friction: only electrons are transferred.
  • Extended: field arrows show the force on a positive charge, so they point towards the negative plate.

4.2bElectric current

Definitions

Electric current
Extended the charge passing a point per unit time.
Conventional current
Extended current flowing from the positive terminal to the negative terminal of the source.
Direct current (d.c.)
current that flows in one direction only.
Alternating current (a.c.)
current that repeatedly reverses its direction.
Ampere (A)
the unit of current.

Key points

  • Electric current is a flow of charge.
  • Current is measured with an ammeter in series; analogue (pointer and scale) or digital, on a suitable range.
  • In metals the current is a flow of free electrons.
  • Extended conventional current flows from + to -; free electrons flow from - to +.
  • Current is not used up: the same current leaves and returns to the cell.
  • Cells and batteries give d.c.; the mains supply is a.c. (50 Hz in the UK).
  • Extended charge = current × time (1 A = 1 C/s), so 2 A for 10 s moves 20 C.
+− A conventional current electrons
Conventional current leaves the + (long) plate; electrons flow the opposite way. The ammeter is in series.
It It d.c.: one way a.c.: reverses
d.c. stays in one direction; a.c. reverses direction repeatedly.

Watch out!

  • Extended: conventional current flows + to -; electron flow is the opposite. Say which one you mean.
  • Current is the same before and after a lamp: it is energy that the lamp transfers, not current.

4.2cElectromotive force and potential difference

Definitions

Electromotive force (e.m.f.)
the electrical work done by a source in moving unit charge around a complete circuit.
Potential difference (p.d.)
the work done by unit charge passing through a component.
Volt (V)
Extended one joule per coulomb (1 V = 1 J/C).

Key points

  • Both e.m.f. and p.d. are measured in volts with a voltmeter in parallel (across the component).
  • e.m.f. is energy given to each coulomb by the source; p.d. is energy transferred from each coulomb by a component.
  • Voltmeters may be analogue or digital, used on a suitable range; read analogue scales at eye level to avoid parallax.
  • Beyond the syllabus: an ideal voltmeter has a very high resistance so it takes almost no current.
  • Extended 1 V means 1 J of work per coulomb; a 12 V battery gives each coulomb 12 J.
A V A: series V: parallel
Ammeter in series with the lamp; voltmeter in parallel across it.

Watch out!

  • Voltmeter across (parallel), ammeter in line (series). Swapping them is a classic lost mark.
  • p.d. is across a component, current is through it. Never say "voltage through".

4.2dResistance

Definitions

Resistance
the ratio of the p.d. across a component to the current through it (R = V/I).
Ohm (Ω)
the unit of resistance; 1 Ω = 1 V/A.
Ohmic conductor
Beyond the syllabus: a conductor whose current is directly proportional to the p.d. across it at constant temperature.
Diode
Extended a component that allows current in one direction only.

Key points

  • Measure R: ammeter in series, voltmeter across the resistor, vary the current with a variable resistor; R = V/I.
  • Extended fixed resistor (constant temperature): I-V graph is a straight line through the origin.
  • Extended filament lamp: curve flattens, because the hot filament has higher resistance.
  • Longer wire: more resistance. Thicker wire (larger cross-sectional area): less resistance.
  • Extended diode conducts in the forward direction only (very high resistance in reverse).
  • Extended R ∝ L and R ∝ 1/A: doubling the length doubles R; doubling the area halves R.
VI resistor filament lamp
Extended: I-V graphs: a resistor (blue) is a straight line through the origin; the lamp curve (red) flattens as the filament heats up.
VI forward:conducts reverse: I = 0 diode
Extended: a diode conducts in the forward direction only; in reverse the current is zero.
rheostat A R V
Measuring resistance: the rheostat varies the current; record V and I and calculate R = V/I.

Watch out!

  • Extended: lamp resistance increases with current (hotter filament); do not call the lamp ohmic.
  • A thicker wire has less resistance, not more.

4.2eElectrical energy and electrical power

Definitions

Power
the rate of energy transfer (energy transferred per unit time).
Kilowatt-hour (kWh)
the energy transferred by a 1 kW appliance in 1 hour (= 3.6 × 106 J).

Key points

  • Electric circuits transfer energy from the cell or mains to the surroundings via the components.
  • Power of an appliance = current × p.d.
  • Energy in joules: use power in W and time in s.
  • Energy in kWh: use power in kW and time in hours.
  • Cost = number of kWh (units) × price per kWh.
heater 2000 W= 2 kW on for 90 min= 1.5 h E = 2 × 1.5 = 3 kWh cost = 3 × 30p = 90p
Worked kWh cost: convert watts to kilowatts and minutes to hours before multiplying.

Watch out!

  • Mixing units: kWh needs kW and hours; joules need W and seconds.
  • The kWh is a unit of energy, not power.

4.3aCircuit diagrams and circuit components

Definitions

Thermistor
a resistor whose resistance decreases as its temperature increases.
Light-dependent resistor (LDR)
a resistor whose resistance decreases as the light intensity increases.
Variable resistor (rheostat)
a resistor whose resistance can be changed, used to control the current.
Relay
a switch operated by an electromagnet, so a small current can switch a large current.
Light-emitting diode (LED)
Extended a diode that emits light when current flows through it in the forward direction.

Key points

  • Draw circuits with a ruler, straight wires and square corners, no gaps at junctions.
  • Mark junctions with a dot; wires that cross without a dot are not connected.
  • Cell: the long plate is positive. A battery is two or more cells in series.
  • Know the symbols for: cell, battery, switch, lamp, resistor, variable resistor, thermistor, LDR, heater, fuse, ammeter, voltmeter, motor, generator, power supply, potential divider, bell, magnetising coil, relay, transformer.
  • Extended know the diode and LED symbols; the diode arrow points in the direction of conventional current it allows.
cell battery switch lamp resistor variableresistor fuse heater
Circuit symbols (1): sources, switch, lamp and resistors.
A ammeter V voltmeter thermistor LDR diode LED M motor G generator
Circuit symbols (2): meters, sensors, diodes (Extended), motor and generator.

Watch out!

  • A lamp symbol is a circle with a cross; a circle with a letter is a meter, motor or generator.
  • Forgetting the junction dot where a voltmeter joins the circuit.

4.3bSeries and parallel circuits

Definitions

Series circuit
components connected one after another in a single loop, so the same current passes through each.
Parallel circuit
components connected on separate branches between the same two points.
Conservation of charge at a junction
Extended the sum of the currents into a junction equals the sum of the currents out of it.

Key points

  • Series: the current is the same at every point.
  • Series: total resistance is the sum of the resistances; e.m.f.s of cells in series add.
  • Parallel: the current from the source is larger than the current in any branch.
  • Parallel: the combined resistance of two resistors is less than either resistor alone.
  • Lamps in parallel: each gets the full p.d., and each can be switched independently; one failing leaves the rest on.
  • Extended in series the p.d.s across the components add up to the supply p.d.
  • Extended the p.d. across each parallel branch is the same as the p.d. across the whole parallel arrangement.
  • Extended in parallel the branch currents add up to the supply current (charge is conserved).
6 V A A 0.2 A0.2 A 10 Ω20 Ω 2 V4 V 2 V + 4 V = 6 V
Series: one current (0.2 A) everywhere; the 6 V supply is shared 2 V + 4 V in the ratio of the resistances.
6 V 0.9 A 10 Ω20 Ω 0.6 A0.3 A 6 V across each branch
Parallel: each branch gets the full 6 V; branch currents 0.6 A + 0.3 A add to 0.9 A from the cell.

Watch out!

  • Adding a resistor in parallel lowers the total resistance: two 10 Ω in parallel make 5 Ω, not 20 Ω.
  • Current is not used up along a series circuit; it is the same before and after each component.

4.3cAction and use of circuit components

Definitions

Potential divider
two resistors in series across a supply, so the supply p.d. is shared between them.
Variable potential divider (potentiometer)
Extended a potential divider whose output p.d. can be varied continuously, e.g. by a sliding contact.

Key points

  • For a constant current, the p.d. across a conductor increases as its resistance increases.
  • In a potential divider the larger resistor takes the larger share of the supply p.d.
  • Extended moving the slider of a variable potential divider varies Vout from 0 to the full supply p.d.
  • Heat a thermistor: its R falls, so its share of the p.d. falls (and the other resistor’s rises).
  • Light on an LDR: its R falls, so its share of the p.d. falls. Used for automatic street lights.
  • Extended V1/V2 = R1/R2; the output can switch a relay or LED at a set temperature or light level.
6 V R1 R2 Vout
Potential divider: Vout is the p.d. across R2. Replace R2 with a thermistor or LDR to make a sensor.
Rtemperature thermistor Rlight intensity LDR
Sensor resistors: a thermistor’s resistance falls as temperature rises; an LDR’s falls as light intensity rises.

Watch out!

  • The bigger resistor gets the bigger p.d., not the smaller one.
  • Hot thermistor or bright LDR means lower resistance, not higher.

4.4Electrical safety

Definitions

Fuse
a thin wire in the live wire that melts and breaks the circuit when the current exceeds its rating.
Circuit breaker (trip switch)
an automatic switch that breaks the circuit when the current is too large; it can be reset.
Earth wire
a low-resistance path to earth, connected to the metal case of an appliance.
Double insulation
an appliance with a non-conducting outer case and no exposed metal, so it needs no earth wire.

Key points

  • Hazards: damaged insulation, overheated cables (current too high), damp conditions, overloaded plugs and sockets.
  • Mains wires: live (brown, at high p.d.), neutral (blue, near 0 V), earth (green and yellow).
  • Fuses and switches go in the live wire, so the appliance is disconnected from the high p.d. when off or blown.
  • Fault: live touches a metal case, a large current flows to earth and the fuse melts, so the case is never live.
  • Choose the fuse rating (or trip-switch setting) just above the normal working current (common fuse ratings 3 A, 5 A, 13 A).
  • Circuit breakers act faster than fuses and are reset, not replaced.
  • For a double-insulated appliance (no earth wire), the fuse still protects the circuit and the cabling.
earth neutral live fuse cable grip
Three-pin plug: the fuse sits in the live wire; the earth pin connects to the metal case.
metal case livefuse fault large currentblows fuse earth wire
Earthing: if the live wire touches the metal case, a large current flows to earth and blows the fuse.

Watch out!

  • A fuse rated far above the working current gives no protection: a 2.6 A lamp needs a 3 A fuse, not 13 A.
  • The fuse must be in the live wire; in the neutral the appliance stays live after it blows.

4.5aElectromagnetic induction

Definitions

Electromagnetic induction
the production of an e.m.f. in a conductor when it cuts magnetic field lines or when the magnetic field through it changes.
Direction of induced e.m.f. (Lenz)
Extended the induced e.m.f. (and current) is in a direction that opposes the change producing it.
Fleming’s right-hand rule
Extended thumb = motion, first finger = field, second finger = induced current (generators).

Key points

  • Move a magnet into a coil, or a wire through a field: a sensitive meter deflects.
  • No relative movement (no change in field) means no e.m.f.
  • Reversing the motion or the magnet’s poles reverses the e.m.f.
  • Bigger e.m.f.: faster movement, stronger magnet, more turns on the coil.
  • Extended pushing N into a coil makes the near end of the coil an N pole, which repels the magnet (opposes the change).
  • Extended work done against this opposing force is transferred as electrical energy.
SN push in sensitive meter near end becomes N Extended:
Pushing the magnet in induces an e.m.f.; the meter deflects. Pulling it out gives the opposite deflection.
NS motion field induced current into the page
Extended: wire moved up through a field from N to S; by the right-hand rule the induced current flows into the page.

Watch out!

  • A stationary magnet inside a coil induces nothing: the field must be changing.
  • Extended: the induced pole opposes the motion (N facing an approaching N), never helps it.

4.5bThe a.c. generator Extended

Definitions

a.c. generator
Extended a coil rotating in a magnetic field, connected to the external circuit through slip rings and brushes, producing an alternating e.m.f.
Slip rings
Extended two complete rings on the axle, each connected to one end of the coil, that keep the coil in contact with the brushes.

Key points

  • Extended rotating coil cuts field lines, so an e.m.f. is induced.
  • Extended each side of the coil moves up then down every turn, so the e.m.f. reverses every half turn: a.c.
  • Extended slip rings and carbon brushes connect the rotating coil to the outside circuit.
  • Extended faster rotation: larger peak e.m.f. and higher frequency. Stronger field or more turns: larger peak.
  • Extended e.m.f. is maximum when the coil plane is parallel to the field (sides cut lines fastest).
  • Extended e.m.f. is zero when the coil plane is perpendicular to the field (sides move along the lines).
NS coil a.c. output slip rings brushes
Extended: simple a.c. generator: the coil turns between the poles; slip rings and brushes carry the a.c. out.
e.m.f.t max: coil parallel to field zero: coil perpendicular to field
Extended: e.m.f. against time: peaks when the coil is parallel to the field, zero when perpendicular.

Watch out!

  • Extended: a generator uses slip rings (a.c.); a d.c. motor uses a split-ring commutator. Do not swap them.
  • Extended: maximum e.m.f. is when the coil is parallel (horizontal) to the field, not perpendicular.

4.5cMagnetic effect of a current

Definitions

Solenoid
a long coil of wire; when it carries a current its field is like that of a bar magnet.
Electromagnet
a solenoid wound on a soft-iron core, magnetised only while current flows.
Right-hand grip rule
grip the wire with the thumb along the current: the curled fingers give the field direction.

Key points

  • Straight wire: field lines are concentric circles round the wire.
  • Solenoid: field like a bar magnet outside; lines run parallel inside.
  • Find the pattern with iron filings or plotting compasses on card round the wire or solenoid; compasses give the direction.
  • Extended larger current gives a stronger field; reversing the current reverses the field.
  • More turns and a soft-iron core make an electromagnet stronger.
  • Uses: relays (small current switches a large one), loudspeakers (a.c. in a coil makes the cone vibrate), lifting magnets.
  • Extended field of a wire is weaker further from the wire (circles spread out).
  • Extended solenoid field is strongest (and uniform) inside and weaker outside, especially beyond the ends.
current outof the page circles spreadout = weaker
Straight wire, current out of the page: circular field lines, anticlockwise, spreading out with distance.
NS uniform field inside
Solenoid: bar-magnet pattern outside, strong uniform field inside. Reverse the current to swap N and S.
coil contacts M low-current circuit high-current circuit
Relay: closing the switch energises the coil; the iron core pulls the contacts shut and the high-current circuit runs the motor.

Watch out!

  • Field lines round a wire are circles, not lines radiating out from the wire.
  • An electromagnet core must be soft iron (steel would stay magnetised when switched off).

4.5dForce on a current-carrying conductor

Definitions

Motor effect
a current-carrying conductor in a magnetic field experiences a force.
Fleming’s left-hand rule
Extended thumb = force (motion), first finger = field (N to S), second finger = current (+ to -).

Key points

  • Extended force is largest when the current is perpendicular to the field; zero when parallel.
  • Reversing the current or the field reverses the force (reversing both leaves it unchanged).
  • Bigger current or stronger field gives a bigger force.
  • Demo: a loose wire between the poles of a U-shaped magnet jumps when the current is switched on.
  • Extended beams of charged particles are also deflected, since a moving charge is a current.
  • Extended for an electron beam, the conventional current is opposite to the beam direction.
NS force field current out of the page
Motor effect: field N to S, current out of the page, so the force on the wire is upwards.
thuMb: Motion (force) First finger: Field seCond finger: Current left hand
Extended: Fleming’s left-hand rule. Hold thumb, first and second fingers at right angles.
××××× ××××× ××××× ××××× electron beam force field into the page
Extended: an electron beam in a field into the page curves (here downwards); the force is always at right angles to its motion.

Watch out!

  • Extended: use the left hand for motors (force) and the right hand for generators (induced current).
  • Extended: for electrons point the second finger opposite to their motion.

4.5eThe d.c. motor

Definitions

Split-ring commutator
Extended a split ring on the axle that reverses the current in the coil every half turn.
Brushes
Extended carbon contacts that press on the commutator (or slip rings) to connect the rotating coil to the circuit.

Key points

  • Current in a coil in a field: forces on the two sides act in opposite directions, giving a turning effect.
  • Turning effect increases with more turns, larger current and a stronger field.
  • Reversing the current or the field reverses the direction of rotation.
  • Extended the commutator reverses the current every half turn (when the coil is vertical), so the coil keeps turning the same way.
  • Extended momentum carries the coil past the vertical, where the force gives no turning effect.
NS FF split ring brush
d.c. motor: forces up on one side and down on the other turn the coil; the split ring and brushes feed the current.
NS FF field from N to S
End view: current into the page on the left side, out on the right; forces down and up make the coil turn anticlockwise.

Watch out!

  • Extended: the commutator reverses the current in the coil, not in the external circuit.
  • Opposite sides of the coil carry current in opposite directions, so the forces are opposite (a turning pair).

4.5fThe transformer

Definitions

Transformer
two coils (primary and secondary) wound on a soft-iron core, used to change the size of an alternating voltage.
Step-up transformer
a transformer with more turns on the secondary than the primary, so Vs > Vp.
Step-down transformer
a transformer with fewer turns on the secondary than the primary, so Vs < Vp.

Key points

  • Transformers work only on a.c.
  • The voltage ratio equals the turns ratio.
  • Power is transmitted at high voltage: step up at the power station, step down near homes.
  • High voltage means small current, so less energy is lost as heat in the cables and thinner, cheaper cables can be used.
  • Extended a.c. in the primary makes a changing magnetic field in the soft-iron core; this changing field through the secondary induces an alternating e.m.f.
  • Extended an ideal (100% efficient) transformer has power in = power out.
  • Extended cable power loss = I2R, so halving the current quarters the loss.
a.c. ina.c. out primary secondary soft-iron core Ns > Np: step-up
Step-up transformer: more turns on the secondary, so the output voltage is larger.
power station25 kV step-uptransformer cables at 400 kV small I, low I²R loss step-downtransformer homes230 V
The grid: step up for transmission (small current, low I2R loss), step down for safe use in homes.

Watch out!

  • A transformer does not work on d.c.: a steady current gives a constant field and no induced e.m.f.
  • Stepping up the voltage steps down the current; it does not create energy.
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