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All revision notes Revision notes · ElectromagnetismElectromagnetism revision notes
Charge and electric fields, current, potential difference and resistance, circuits, magnets, motors, induction, mains electricity and the National Grid. Each section follows one lesson: what you need to know, key terms, the equations with units, a worked example, common mistakes and an exam tip.
1 Electric Charge
What you need to know
Push or Pull
- There are two kinds of charge, positive and negative. Like charges repel; unlike charges attract.
- Charge comes from electrons (negative) and protons (positive). A neutral object has equal numbers of each; it becomes charged by gaining or losing electrons.
- The forces between two charged objects are equal in size and opposite in direction, one on each object, whatever the two charges are.
Distance
- The force between two charges gets weaker quickly with distance: twice as far apart gives a quarter of the force, three times as far a ninth (an inverse square law).
- The force is proportional to each charge: double one charge and the force doubles. This is Coulomb's law, F = kq₁q₂ ÷ r².
Field Lines
- An electric field is a region where a charge feels a force. The direction of the field is the direction of the force on a small positive charge.
- Field lines point straight out from a positive point charge and straight into a negative one. The closer the lines, the stronger the field.
- Between two parallel charged plates the field is uniform: parallel, evenly spaced lines from the positive plate to the negative plate.
Key terms
- Charge
- a property of electrons (negative) and protons (positive), measured in coulombs (C)
- Electric field
- a region in which a charge experiences a force
- Field line
- a line showing the direction of the force on a small positive charge
- Inverse square law
- a quantity that falls with 1 ÷ distance²: twice as far, a quarter as much
Equations
| Equation | What it says, symbols and units |
|---|---|
Fe = kq1q2r2 | Two charges attract or repel with an inverse-square force. k = 8.99 × 10⁹ N m²/C².
Beyond IGCSE and GCSE: AP Physics 2 and NGSS HS-PS2-4. IGCSE and GCSE need only like/unlike charges and field patterns. |
Diagram to know
Field patterns: lines radiating out from a single positive charge (arrows outwards), into a single negative charge (arrows inwards), and from the positive to the negative plate of a pair of parallel plates (straight, parallel, evenly spaced, with curved edges at the ends).
Worked example
Two small spheres each carry +20 nC, with their centres 6.0 cm apart. Calculate the force between them, then the force when they are moved to 12 cm apart. (k = 8.99 × 109 N m²/C²; AP Physics 2 and NGSS.)
- Convert: q = 20 × 10−9 C, r = 0.060 m.
- F = kq₁q₂ ÷ r² = 8.99 × 109 × (20 × 10−9)² ÷ 0.060² = 1.0 × 10−3 N, a repulsion (like charges).
- At 12 cm the distance has doubled, so the force falls to a quarter: 1.0 mN ÷ 4 = 0.25 mN.
Answer: 1.0 mN at 6.0 cm; 0.25 mN at 12 cm, both repulsive
Common mistakes
- Saying a positive object has gained protons. Only electrons move; a positive object has lost electrons.
- Drawing field lines from negative to positive. They go from positive to negative, the way a positive charge is pushed.
- Halving the force when the distance doubles. It falls to a quarter.
Exam tip
When you draw a field pattern, put arrows on every line, start and end the lines on the charges, and never let two lines cross. Each of these is checked by the mark scheme.
AP Physics and NGSS: AP Physics 1 has no electrostatics; AP Physics 2 (Unit 10) uses Coulomb's law with vectors, adds the forces from several charges, and links field lines to electric potential. NGSS HS-PS2-4 asks you to use the inverse square laws of both gravity and electric force.
2 Conductors & Insulators
What you need to know
Rubbing
- Rubbing two insulators together moves electrons from one to the other. The one that gains electrons becomes negative; the other is left positive by the same amount.
- A polythene strip rubbed with a wool duster gains electrons (negative); an acetate strip loses electrons to the duster (positive). Protons never move: they are locked in the nuclei.
Conductors
- Conductors, such as metals and graphite, have free electrons that move through them easily, so charge flows away at once. Insulators, such as plastic, glass, rubber and dry wood, hold their charge where it is.
- Damp materials such as wet string are poor conductors: charge leaks away slowly. A charged gold-leaf electroscope shows the difference: its leaf falls at once when touched by a conductor.
Induction
- A charged rod brought near a neutral conductor pushes or pulls its free electrons: a negative rod pushes them to the far side, leaving the near side positive. This is charging by induction.
- The near side is closer to the rod, so its attraction beats the repulsion of the far side: a charged object attracts small neutral objects (paper, dust, an empty can).
- If the conductor then touches the rod, electrons cross over, both carry the same sign and they repel.
Earthing
- Earthing joins a conductor to the ground with another conductor, so charge can flow away and it cannot build up.
- Electrons flow from a negative object into the ground, or up from the ground onto a positive object, until it is neutral.
- Charge building up on moving belts, fuel pipes or aircraft can make a spark that ignites dust or vapour, so these are earthed before use.
Key terms
- Conductor
- a material through which charge flows easily, because it has free electrons
- Insulator
- a material through which charge cannot flow easily
- Induction (electrostatic)
- separating the charges in an object by bringing a charged object near it, without touching
- Earthing
- connecting an object to the ground with a conductor so charge can flow away
Equations
| Equation | What it says, symbols and units |
|---|---|
Q = ne | A charge is a whole number of electron charges.
Not a listed IGCSE or GCSE equation; useful for AP Physics 2 and for counting electrons. |
Diagram to know
A negative rod held near a neutral metal can: minus signs gathered on the far side of the can, plus signs on the near side, and an arrow showing the can pulled towards the rod.
Worked example
A polythene strip rubbed with a duster gains a charge of −40 nC. How many electrons has it gained, and what is the charge on the duster? (e = 1.6 × 10−19 C)
- Number of electrons = charge ÷ charge of one electron = 40 × 10−9 ÷ 1.6 × 10−19 = 2.5 × 1011.
- The duster lost exactly those electrons, so its charge is the same size with the opposite sign: +40 nC.
Answer: 2.5 × 1011 electrons; the duster is +40 nC
Common mistakes
- Saying positive charge (protons) moves onto or off an object. In solids only electrons move.
- Saying a neutral object has no charges. It has equal amounts of positive and negative charge.
- Saying an insulator is charged by rubbing because it conducts. It keeps the charge because it does not.
Exam tip
In "explain" questions on static, always say which way the electrons moved and what that leaves behind ("electrons move from the duster to the strip, so the strip is negative and the duster is left positive"). Examiners do not credit "charge moves" on its own.
AP Physics and NGSS: AP Physics 1 has no electrostatics. AP Physics 2 adds charge conservation in multi-step charging and the idea that excess charge sits on the outside surface of a conductor. NGSS HS-PS2-6 asks why the electrical structure of materials suits them to a job, such as copper wires inside plastic insulation.
3 Current, Voltage & Ohm's Law
What you need to know
Current
- Current is the rate of flow of charge: I = Q ÷ t, in amperes. 1 A is 1 coulomb passing a point each second.
- In a metal the current is a flow of free electrons. Conventional current is shown from + to − round the circuit; the electrons actually drift the other way.
- In a single loop the current is the same everywhere. A lamp transfers energy; it does not use up current. Measure current with an ammeter in series.
Potential Difference
- Potential difference (p.d.) is the energy transferred per unit charge: V = W ÷ Q, so 1 V is 1 J per coulomb. Measure it with a voltmeter in parallel, across the component.
- The electromotive force (e.m.f.) of a cell is the energy it gives each coulomb that passes through it.
- Cells in series add their e.m.f.s when they face the same way; a cell turned round subtracts its e.m.f.
Resistance
- Resistance R = V ÷ I, in ohms (Ω). The bigger the resistance, the smaller the current for the same p.d.
- A resistor at constant temperature gives a straight-line current–p.d. graph through the origin: current is proportional to p.d. (it obeys Ohm's law).
- A filament lamp's graph curves over: as it heats up its resistance rises. A diode lets current through in one direction only.
Key terms
- Current
- the rate of flow of charge, in amperes (A)
- Potential difference
- the energy transferred per coulomb between two points, in volts (V)
- Electromotive force
- the energy a source gives each coulomb of charge, in volts
- Resistance
- the p.d. needed per ampere of current, in ohms (Ω)
- Ohmic conductor
- a component whose current is proportional to the p.d., at constant temperature
Equations
| Equation | What it says, symbols and units |
|---|---|
I = Qt | Current is the charge passing a point each second.
|
V = WQ | Potential difference is the energy each coulomb transfers as it passes through a component.
|
E = QV | Energy transferred is the charge times the potential difference it moves through.
|
V = IR | Potential difference is current times resistance.
|
Diagram to know
Current–p.d. graphs for three components: a resistor (straight line through the origin), a filament lamp (an S-shape that flattens at both ends) and a diode (zero current for negative p.d., then a steep rise above about 0.6 V).
Worked example
A lamp with 3.0 V across it carries a current of 0.25 A for 20 s. Calculate the charge that flows, the energy transferred and the lamp's resistance.
- Q = It = 0.25 × 20 = 5.0 C.
- Energy transferred E = QV = 5.0 × 3.0 = 15 J.
- R = V ÷ I = 3.0 ÷ 0.25 = 12 Ω.
Answer: 5.0 C; 15 J; 12 Ω
Common mistakes
- Saying the current is used up by a lamp, so it is smaller after it. In a series loop the current is the same everywhere.
- Connecting a voltmeter in series or an ammeter in parallel.
- Calling a filament lamp ohmic. Its resistance rises as it gets hotter.
Exam tip
To describe an I–V graph, use the words "directly proportional" only for a straight line through the origin, and say what happens to the resistance ("the gradient falls, so the resistance increases as the filament heats up").
AP Physics and NGSS: AP Physics 1 does not cover circuits; AP Physics 2 (Unit 11) adds resistivity, internal resistance and terminal voltage. NGSS HS-PS3-3 uses circuits as devices that convert energy.
4 Magnets & Electromagnets
What you need to know
Poles and Magnetic Materials
- A magnet has two poles, north (N) and south (S). Like poles repel; unlike poles attract. Repulsion is the only sure test that something is a magnet.
- Magnetic materials are iron, steel, nickel and cobalt. A magnet attracts them with either pole. Aluminium and copper are not magnetic.
- A piece of iron or steel near a magnet becomes an induced magnet. Soft iron loses its magnetism when the magnet is removed (a temporary magnet); steel keeps it (a permanent magnet).
Mapping a Magnet's Field
- A magnetic field is a region where a magnetic material or a magnet feels a force. Field lines go from the N pole to the S pole outside the magnet.
- The field is strongest at the poles, where the lines are closest. Plot it with a small compass, moving it along step by step, or show it with iron filings.
- A compass needle is a small magnet that lines up with the field: the Earth's magnetic field makes it point north.
The Field of a Coil
- A current in a wire makes a magnetic field: circles centred on the wire, strongest close to it. Reversing the current reverses the field.
- A coil (solenoid) has a field like a bar magnet's, strongest and nearly uniform inside. The right-hand grip rule gives its direction: fingers curl with the current, the thumb points to the N end.
Build an Electromagnet
- An electromagnet is a coil wrapped round a soft iron core. Its field is made stronger by more turns, a bigger current and an iron core.
- Soft iron is used because it magnetises strongly and loses its magnetism when the current is switched off, so the magnet can let go.
Relays
- A relay is a switch worked by an electromagnet: a small current in its coil pulls an iron armature that closes a second, separate circuit.
- This lets a small, safe current (from a key switch or a sensor) switch on a large current, such as a car starter motor or a 230 V pump.
Key terms
- Magnetic material
- a material attracted by a magnet: iron, steel, nickel or cobalt
- Induced magnetism
- magnetism given to a magnetic material while it is near a magnet
- Magnetic field
- a region in which a magnet or magnetic material feels a force
- Solenoid
- a long coil of wire; with a current it makes a field like a bar magnet's
- Relay
- a switch operated by an electromagnet, joining two separate circuits
Diagram to know
The field of a bar magnet: closed loops leaving the N pole and entering the S pole, crowded at the poles, with arrows from N to S. And the field round a straight wire: concentric circles, wider apart further out, with the direction from the right-hand grip rule.
Worked example
A relay's coil runs on 6.0 V and takes 0.10 A. Its contacts switch a 230 V pump that draws 4.0 A. Find the resistance of the coil and the power of the pump, and say why the relay is used.
- Coil resistance R = V ÷ I = 6.0 ÷ 0.10 = 60 Ω.
- Pump power P = IV = 4.0 × 230 = 920 W.
- The switch and the sensor carry only the coil's 0.10 A at 6.0 V; the 4.0 A at 230 V flows only through the relay's contacts, in a separate circuit.
Answer: 60 Ω; 920 W; a small, low-voltage current safely switches the large mains current
Common mistakes
- Saying a magnet attracts all metals. It attracts only magnetic materials; aluminium, copper and most coins made of them are not.
- Drawing field lines from S to N, or letting them cross.
- Choosing steel for an electromagnet's core. Steel stays magnetised, so the electromagnet could not let go.
Exam tip
When asked how to make an electromagnet stronger, give three separate changes: more turns, more current, an iron core. "Make it bigger" scores nothing.
AP Physics and NGSS: AP Physics 1 does not cover magnetism. AP Physics 2 gives the field round a long wire a size, B = μ₀I ÷ 2πr, and NGSS HS-PS2-5 asks for evidence that a current makes a magnetic field.
5 Electric & Magnetic Fields
What you need to know
Field Strength
- Electric field strength is the force per unit positive charge at a point: E = F ÷ q, in N/C. Three times the charge at the same spot feels three times the force; the field is the same.
- A positive charge is pushed along the field; a negative charge is pushed against it. Between parallel plates the field is uniform, so the force is the same everywhere between them.
The Fading Field
- Round a charged sphere the field points straight out (for a positive charge) and fades with the square of the distance: twice as far, a quarter of the field.
- Doubling the charge doubles the field at every point.
Hovering Drop
- Between parallel plates E = V ÷ d. A charged drop hovers when the electric force balances its weight: qE = mg.
- Millikan's oil-drop measurements showed every charge is a whole number of 1.6 × 10⁻¹⁹ C, the charge of one electron.
The Motor Effect
- A current-carrying wire in a magnetic field feels a force: the motor effect. The force is at right angles to both the current and the field, and reverses if either is reversed.
- Use Fleming's left-hand rule: first finger for the field (N to S), second finger for the current (+ to −), thumb for the force (motion).
- The force is bigger for a bigger current, a stronger field and a longer length of wire in the field: F = BIl, when the wire is at right angles to the field.
Induction & Transformers
- A changing magnetic field through a coil induces a p.d. across it. A steady field induces nothing: a transformer needs alternating current.
- A transformer is two coils on a soft iron core. The alternating current in the primary makes a changing field in the core, which induces an alternating p.d. in the secondary.
- Vₚ ÷ Vₛ = Nₚ ÷ Nₛ. More turns on the secondary steps the voltage up; fewer steps it down.
Key terms
- Electric field strength
- the force on each coulomb of positive charge at a point, in N/C
- Motor effect
- the force on a current-carrying conductor in a magnetic field
- Magnetic flux density
- the strength of a magnetic field, B, in tesla (T)
- Transformer
- two coils on an iron core that change the size of an alternating p.d.
Equations
| Equation | What it says, symbols and units |
|---|---|
E = Fq, E = Vd | Field strength is force per unit charge; between parallel plates it is the p.d. over the gap.
AP Physics 2 and NGSS; not an IGCSE or GCSE equation. |
F = BIl | Force on a current-carrying wire at right angles to a magnetic field.
|
VpVs = NpNs | A transformer changes an alternating voltage in the ratio of its turns.
|
Diagram to know
Fleming's left-hand rule: thumb, first finger and second finger held at right angles, labelled thrust (force), field and current. And a transformer: a closed soft iron core with the primary coil on one side and the secondary on the other, a.c. in and a.c. out.
Worked example
(a) A 5.0 cm length of wire carries 4.0 A at right angles to a 0.20 T magnetic field. Find the force on it. (b) A transformer has 240 turns on its primary and 960 on its secondary. 12 V a.c. goes in. What comes out?
- (a) F = BIl = 0.20 × 4.0 × 0.050 = 0.040 N.
- (b) Vₛ = Vₚ × Nₛ ÷ Nₚ = 12 × 960 ÷ 240 = 48 V, a step-up transformer (four times the turns, four times the p.d.).
Answer: (a) 0.040 N (b) 48 V a.c.
Common mistakes
- Using the right hand for the motor effect. Motors use the left hand.
- Leaving the length in cm in F = BIl.
- Saying a transformer works on d.c. A steady current makes a steady field, which induces nothing.
Exam tip
Before using Fleming's left-hand rule, mark the field direction (N to S) and the current direction (+ to −) on the diagram itself. Most wrong answers come from a field drawn the wrong way round.
AP Physics and NGSS: AP Physics 1 does not cover fields or induction. AP Physics 2 (Units 10 and 12) uses E = F ÷ q and E = V ÷ d with electric potential, and the magnetic force on a moving charge, F = qvB sin θ. NGSS HS-PS2-5 asks for evidence that a current makes a magnetic field and a changing field makes a current.
6 Motors & Loudspeakers
What you need to know
A Coil That Turns
- A coil carrying a current in a magnetic field turns, because the current flows in opposite directions along its two sides: one side is pushed up, the other down.
- The turning effect is bigger with more turns on the coil, a bigger current or a stronger magnetic field.
The d.c. Motor
- On slip rings a coil only rocks to the upright position and stops. A split-ring commutator reverses the current in the coil every half turn, so the forces always turn it the same way and it keeps spinning.
- Carbon brushes press on the commutator to carry current in and out. Reversing the current or the magnets reverses the direction of spin.
- A practical motor turns faster with more turns, a bigger current or a stronger field; a curved soft iron core inside the coil strengthens the field.
The Loudspeaker
- In a loudspeaker, an alternating current in a coil sitting in a permanent magnet's field makes the coil and the cone move in and out (the motor effect).
- The cone vibrates at the frequency of the current, making a sound wave. A higher frequency gives a higher note; a bigger current gives a bigger movement and a louder sound.
- A steady d.c. current gives just one click as the cone moves once and stays.
Beams in a Magnetic Field
- A beam of charged particles moving through a magnetic field is a current, so it feels a force at right angles to both its motion and the field, and bends.
- An electron beam's conventional current is opposite to its motion, so electrons bend the opposite way to protons in the same field. Use Fleming's left-hand rule with the current direction.
Key terms
- Split-ring commutator
- a split ring that reverses the current in a motor's coil every half turn
- Brushes
- carbon contacts that connect the turning commutator to the circuit
- Loudspeaker
- a device that turns an alternating current into sound using the motor effect
- Fleming's left-hand rule
- thumb = force, first finger = field, second finger = current
Equations
| Equation | What it says, symbols and units |
|---|---|
F = BIl | Force on a current-carrying wire at right angles to a magnetic field.
For a coil, the force on each side is n times that on one wire: F = nBIl. |
Diagram to know
A simple d.c. motor: a rectangular coil between N and S poles, a split-ring commutator on the axle, two brushes connected to a cell, with the forces on the two sides drawn up and down.
Worked example
A motor coil has 20 turns. Each side of the coil is 4.0 cm long, lies at right angles to a 0.10 T field and carries 2.0 A. Find the force on one side of the coil.
- Force on one wire: F = BIl = 0.10 × 2.0 × 0.040 = 0.0080 N.
- There are 20 wires along each side, so the force on one side = 20 × 0.0080 = 0.16 N. The other side has an equal force in the opposite direction, which turns the coil.
Answer: 0.16 N
Common mistakes
- Saying the commutator makes a.c. into d.c. in a motor. In a motor it reverses the current in the coil every half turn.
- Saying a loudspeaker's cone moves faster for a louder sound. A louder sound means a bigger amplitude; the frequency sets the pitch.
- Bending an electron beam the same way as a positive beam.
Exam tip
Explaining why a motor keeps turning takes three linked steps: the forces on the two sides are opposite, so the coil turns; the commutator reverses the current every half turn; so the forces keep turning it the same way.
AP Physics and NGSS: AP Physics 1 does not cover magnetism. AP Physics 2 (Unit 12) calculates the force on a moving charge, F = qvB sin θ, and the radius of its circular path in a field.
7 Induction, Generators & Microphones
What you need to know
Magnet, Coil, Meter
- Moving a magnet into or out of a coil induces an e.m.f., and a current if the circuit is complete. A magnet resting inside the coil induces nothing: the field must be changing.
- The induced e.m.f. is bigger with a faster movement, a stronger magnet or more turns on the coil. Pulling the magnet out, or using the other pole, reverses it.
Which Way? Lenz's Law
- Lenz's law: the induced current flows in the direction that opposes the change causing it. Push an N pole in and the coil's near end becomes an N pole, pushing back.
- So a magnet falls slowly through a copper pipe: the currents induced in the pipe oppose its motion. A non-magnetised slug, or a pipe with a slit, falls at the normal rate.
Alternators and Dynamos
- A coil turning in a magnetic field is a generator. The e.m.f. is biggest when the coil's plane lies along the field (its sides cut the field fastest) and zero when it faces the poles.
- With slip rings it gives alternating current (an alternator); with a split-ring commutator the output never reverses (a dynamo, d.c.).
- Turning it faster gives taller peaks, and more of them each second (a higher frequency).
The Microphone
- A moving-coil microphone is a loudspeaker in reverse: sound waves move a diaphragm and a coil in a magnet's field, inducing a small alternating p.d. that copies the sound.
- A louder sound gives a bigger p.d.; a higher note gives a higher frequency. It needs no battery, but its signal is usually amplified.
Key terms
- Electromagnetic induction
- the production of an e.m.f. across a conductor when the magnetic field through it changes
- Lenz's law
- the induced current opposes the change that produced it
- Alternator
- a generator with slip rings that produces alternating current
- Dynamo
- a generator with a split-ring commutator that produces direct current
Equations
| Equation | What it says, symbols and units |
|---|---|
T = 1f | The period is the time for one complete wave; it is one over the frequency.
For a generator, the frequency of the output equals the number of turns of the coil each second. |
Diagram to know
An alternator: a coil turning between N and S poles, slip rings and brushes to the output, and beside it a graph of e.m.f. against time, a sine wave whose peaks occur when the coil is horizontal (along the field).
Worked example
A power-station generator turns 3000 times a minute. Find the frequency and the period of the alternating p.d. it makes. What happens to these if it turns at 1500 times a minute?
- Turns per second = 3000 ÷ 60 = 50, so the frequency is 50 Hz (one cycle per turn).
- Period T = 1 ÷ f = 1 ÷ 50 = 0.020 s (20 ms).
- At 1500 turns a minute the frequency halves to 25 Hz, the period doubles to 0.040 s, and the peak e.m.f. is smaller because the coil cuts the field more slowly.
Answer: 50 Hz and 0.020 s; at half the speed, 25 Hz and 0.040 s with smaller peaks
Common mistakes
- Saying a stationary magnet inside a coil induces a current. Only a changing field does.
- Saying a faster generator gives the same waveform. Both the peak and the frequency rise.
- Confusing the motor effect (current in, movement out) with induction (movement in, e.m.f. out).
Exam tip
For Lenz's law questions, name the pole the coil makes at the end the magnet approaches ("the end nearest the magnet becomes a north pole, which repels the north pole"). That sentence carries the direction mark.
AP Physics and NGSS: AP Physics 1 does not cover induction. AP Physics 2 (Unit 12) uses magnetic flux, Φ = BA cos θ, and Faraday's law, e.m.f. = −N ΔΦ ÷ Δt, with the minus sign standing for Lenz's law.
8 Electric Circuits
What you need to know
Series
- In a series circuit there is one path: the current is the same through every component.
- The supply p.d. is shared between the components, and the biggest resistance takes the biggest share. The total resistance is the sum: R = R₁ + R₂ + …
- Adding another resistor in series makes the total resistance bigger and the current smaller.
Parallel
- In a parallel circuit each branch has the full supply p.d. The current from the supply is the sum of the branch currents (current is conserved at a junction).
- Each branch can be switched on its own, and one lamp failing leaves the others lit. Adding a branch increases the total current.
- The combined resistance of resistors in parallel is less than the smallest one: 1 ÷ R = 1 ÷ R₁ + 1 ÷ R₂.
Power & Fuses
- Electrical power P = IV, in watts: the rate of energy transfer. An appliance's rating plate gives its power and voltage; the current is I = P ÷ V.
- A fuse in the live wire melts if the current gets too big, breaking the circuit. Choose the smallest standard rating (3 A, 5 A or 13 A) just above the normal current.
The Precipitator
- An electrostatic precipitator puts a high voltage on wires in a chimney. Smoke particles pick up charge and are pulled onto earthed plates, which are rapped so the soot falls into hoppers.
- It brings charge, fields, current and power together: the charged grains are pushed along the field, and the supply's power is P = IV.
Key terms
- Series
- components connected one after another in a single loop
- Parallel
- components connected in separate branches between the same two points
- Power
- the rate of energy transfer, in watts (W)
- Fuse
- a thin wire that melts and breaks the circuit when the current is too large
Equations
| Equation | What it says, symbols and units |
|---|---|
R = R1 + R2 + … | Resistances in series add up; so do the e.m.f.s of cells in series.
|
1R = 1R1 + 1R2 | Two resistors in parallel have less resistance than either one alone.
|
current in = current out (junction); p.d.s add in series; parallel branches share one p.d. | The three rules for sharing current and potential difference in a circuit. |
P = IV | Electrical power is current times potential difference.
|
Diagram to know
Two circuits side by side: two resistors in series with a cell, an ammeter and a voltmeter across each resistor; and two resistors in parallel, with an ammeter in each branch and one in the main line.
Worked example
A 12 Ω and a 6.0 Ω resistor are connected in parallel across a 6.0 V supply. Find the current in each branch, the current from the supply and the combined resistance.
- Each branch has 6.0 V across it: I₁ = 6.0 ÷ 12 = 0.50 A and I₂ = 6.0 ÷ 6.0 = 1.0 A.
- Supply current = 0.50 + 1.0 = 1.5 A.
- Combined resistance R = V ÷ I = 6.0 ÷ 1.5 = 4.0 Ω.
- Check: 1 ÷ R = 1 ÷ 12 + 1 ÷ 6.0 = 0.25, so R = 4.0 Ω, smaller than either resistor.
Answer: 0.50 A and 1.0 A; 1.5 A; 4.0 Ω
Common mistakes
- Adding parallel resistances like series ones. The combined resistance must be less than the smallest branch.
- Saying the current splits equally at every junction. It splits in inverse proportion to the branch resistances.
- Choosing a fuse rating below the normal current, or far above it.
Exam tip
After any parallel-resistance calculation, check that your answer is smaller than the smallest resistor. If it is not, you have added them or forgotten to take the final reciprocal.
AP Physics and NGSS: AP Physics 1 does not cover circuits; AP Physics 2 (Unit 11) uses Kirchhoff's rules on circuits with several loops and cells. NGSS HS-PS3-3 asks you to design a device that converts energy, often a circuit.
9 Circuit Components & Sensors
What you need to know
Circuit Diagrams
- Learn the circuit symbols: cell, battery, switch, lamp, fixed resistor, variable resistor, thermistor, LDR, diode, LED, fuse, motor, ammeter, voltmeter.
- An LED (light-emitting diode) lights only when connected the right way round: the triangle in its symbol points round the loop from + towards −.
- Two identical lamps in series glow equally: the same current passes through both, whichever is nearer the + terminal.
A Wire's Resistance
- The resistance of a wire is proportional to its length and inversely proportional to its cross-sectional area: twice as long, twice the resistance; twice the area, half the resistance.
- A variable resistor (rheostat) changes the length of wire in the circuit to change the current.
Thermistors and LDRs
- A thermistor's resistance falls as its temperature rises (for the usual NTC type). It is used in thermostats and electronic thermometers.
- A light-dependent resistor (LDR)'s resistance falls as the light gets brighter. It is used in automatic lights and light meters.
Potential Dividers
- A potential divider is two resistors in series across a supply. The supply p.d. is shared in the ratio of the resistances: V₁ ÷ V₂ = R₁ ÷ R₂.
- With an LDR or thermistor as one of the two, the output p.d. changes with light or temperature. In the dark an LDR's resistance rises, so its share of the p.d. rises and can switch on a street lamp.
- When the two resistances are equal, each takes half the supply p.d.
Key terms
- Thermistor
- a resistor whose resistance falls as its temperature rises
- Light-dependent resistor
- a resistor whose resistance falls as the light intensity rises
- Potential divider
- two resistors in series that share a supply p.d. in the ratio of their resistances
- Cross-sectional area
- the area of the end face of a wire, in m² (or mm²)
Equations
| Equation | What it says, symbols and units |
|---|---|
R ∝ l and R ∝ 1A | A longer metal wire has more resistance; a thicker one has less.
|
R1R2 = V1V2 | A potential divider shares the supply p.d. in proportion to the two resistances.
|
Diagram to know
A potential divider: a fixed resistor and an LDR in series across a 6.0 V supply, with a voltmeter (the output) across the LDR. Next to it, sketch graphs of thermistor resistance against temperature and LDR resistance against light intensity, both curves falling.
Worked example
An LDR and a 2.0 kΩ resistor are in series across a 6.0 V supply. At dusk the LDR's resistance is 10 kΩ. Find the p.d. across the LDR and the current. What happens to the p.d. across the LDR as it gets darker?
- Total resistance = 10 + 2.0 = 12 kΩ.
- The LDR's share: V = 6.0 × 10 ÷ 12 = 5.0 V (the resistor has the other 1.0 V).
- Current I = 6.0 ÷ 12 000 = 0.00050 A = 0.50 mA.
- As it gets darker the LDR's resistance rises, so its share of the 6.0 V rises above 5.0 V.
Answer: 5.0 V; 0.50 mA; the p.d. across the LDR rises
Common mistakes
- Saying a thermistor's resistance rises with temperature. For the thermistors in these courses it falls.
- Doubling the resistance when a wire's diameter doubles. Its area goes up four times, so the resistance falls to a quarter.
- Splitting a potential divider's p.d. in the wrong ratio: the bigger resistance takes the bigger share.
Exam tip
In sensor-circuit questions, write a chain of three: what changes (it gets darker), what that does to the sensor (the LDR's resistance rises), and what that does to the output (its share of the p.d. rises). Each link is usually one mark.
AP Physics and NGSS: AP Physics 1 does not cover circuits; AP Physics 2 (Unit 11) uses resistivity, R = ρL ÷ A, to calculate a wire's resistance.
10 Electricity at Home
What you need to know
The Heating Effect
- A current heats a wire: electrons collide with the ions of the metal and transfer energy. The heating power is P = I²R, so doubling the current gives four times the heating.
- For the same current, a thinner core (more resistance) heats more. A cable's current rating keeps it below the temperature at which its insulation softens.
Paying for Energy
- Energy transferred = power × time, E = Pt. In joules use W and s; on a bill use kW and hours, giving kilowatt-hours (kW h).
- 1 kW h = 1000 W × 3600 s = 3.6 × 10⁶ J. Cost = number of kW h × price per kW h.
- A low-power device on for a long time can use more energy than a high-power one used briefly.
a.c. and d.c.
- Direct current (d.c.) flows one way only, as from a cell; its trace on an oscilloscope is a flat line. Alternating current (a.c.) keeps reversing direction; its trace is a wave above and below zero.
- UK mains is a.c. at 230 V and 50 Hz: one cycle every 20 ms.
Live, Neutral, Earth
- A mains plug has three wires: live (brown, at 230 V), neutral (blue, near 0 V) and earth (green and yellow, a safety wire joined to the metal case).
- Switches and fuses go in the live wire, so that when they are off or blown the appliance is disconnected from 230 V.
- If the live wire touches an earthed metal case, a large current flows to earth and the fuse melts (or a circuit breaker trips). Double-insulated appliances with plastic cases need no earth wire. A residual current device cuts the supply if current leaks to earth.
Key terms
- Kilowatt-hour
- the energy a 1 kW device transfers in 1 hour, 3.6 × 10⁶ J
- Alternating current
- current that repeatedly reverses direction
- Live wire
- the wire at a high p.d. (230 V in the UK) that carries the supply
- Earth wire
- a safety wire that connects a metal case to the ground
- Double insulation
- an outer case of insulating material, so no earth wire is needed
Equations
| Equation | What it says, symbols and units |
|---|---|
P = I2R | Power lost heating a resistance; a smaller current wastes much less, which is why the grid uses high voltage.
|
E = Pt | Energy transferred is power times time.
|
E = IVt | Energy an electric current transfers in a time t.
|
energy (kW h) = power (kW) × time (h) | The kilowatt-hour is the unit on an electricity bill: cost = energy in kW h × price per kW h. |
Diagram to know
A wired three-pin plug: brown live wire to the fuse and the right-hand pin, blue neutral to the left pin, green-and-yellow earth to the top pin, with the cable grip across the outer sheath.
Worked example
Electricity costs 25p per kW h. Compare a 2.0 kW kettle used for 3 minutes with a 10 W LED lamp left on for 24 hours. Give the kettle's energy in joules too.
- Kettle: E = 2.0 kW × (3 ÷ 60) h = 0.10 kW h, costing 0.10 × 25 = 2.5p.
- In joules: 2000 W × 180 s = 360 000 J.
- Lamp: E = 0.010 kW × 24 h = 0.24 kW h, costing 0.24 × 25 = 6.0p.
- The lamp uses more energy: low power for a long time.
Answer: Kettle 0.10 kW h (2.5p, 360 000 J); lamp 0.24 kW h (6.0p)
Common mistakes
- Putting minutes or watts into the kW h formula. Use kilowatts and hours.
- Saying the earth wire carries current all the time. It carries current only when there is a fault.
- Putting the switch or fuse in the neutral wire. The appliance would still be at 230 V when switched off.
Exam tip
In a fault question, give the full sequence: the live wire touches the case, a large current flows through the earth wire, the fuse melts and disconnects the live supply, so the case is no longer live. Missing any step usually loses a mark.
AP Physics and NGSS: AP Physics 1 does not cover mains electricity. NGSS HS-PS3-2 and HS-PS3-3 use the heating effect and energy costs as examples of energy transfer in devices.
11 The National Grid
What you need to know
Why Such High Voltage?
- Current in transmission cables heats them and wastes energy at a rate P = I²R. For the same power (P = IV), a higher voltage means a smaller current.
- Ten times the voltage gives a tenth of the current and so a hundredth of the heating in the cables. That is why the grid transmits at hundreds of thousands of volts.
Building the Grid
- Step-up transformers at the power station raise the voltage for transmission; step-down transformers at substations lower it, in stages, for factories and finally to 230 V for homes.
- The step-down must undo the step-up: the turns ratios set the voltages, Vₚ ÷ Vₛ = Nₚ ÷ Nₛ.
- For an ideal (100% efficient) transformer the power in equals the power out, IₚVₚ = IₛVₛ: stepping the voltage down steps the current up.
Key terms
- National Grid
- the network of cables and transformers linking power stations to consumers
- Step-up transformer
- a transformer with more turns on the secondary, so it raises the p.d.
- Step-down transformer
- a transformer with fewer turns on the secondary, so it lowers the p.d.
- Transmission loss
- energy wasted as heat in the cables, at a rate I²R
Equations
| Equation | What it says, symbols and units |
|---|---|
P = I2R | Power lost heating a resistance; a smaller current wastes much less, which is why the grid uses high voltage.
|
VpVs = NpNs | A transformer changes an alternating voltage in the ratio of its turns.
|
IpVp = IsVs | For a 100% efficient transformer, power in equals power out: step the voltage up and the current goes down.
|
Diagram to know
The grid as a chain: power station, step-up transformer, high-voltage transmission cables on pylons, step-down transformer at a substation, lower-voltage distribution cables, a final step-down transformer, then homes at 230 V.
Worked example
A power station sends 500 kW along cables with a total resistance of 5.0 Ω. Find the power wasted in the cables at 25 kV and at 250 kV.
- At 25 kV: I = P ÷ V = 500 000 ÷ 25 000 = 20 A. Power wasted = I²R = 20² × 5.0 = 2000 W.
- At 250 kV: I = 500 000 ÷ 250 000 = 2.0 A. Power wasted = 2.0² × 5.0 = 20 W.
- Ten times the voltage gives a tenth of the current and a hundredth of the loss.
Answer: 2000 W at 25 kV; 20 W at 250 kV
Common mistakes
- Saying high voltage reduces the resistance of the cables. It reduces the current; the resistance is unchanged.
- Saying a step-down transformer reduces the power. Ideally the power is the same; the voltage falls and the current rises.
- Using the full transmission voltage in I²R or V²/R for the cable. The p.d. across the cable itself is much smaller.
Exam tip
"Explain why the grid uses high voltages" is a three-step chain: for the same power, a higher voltage means a lower current; a lower current means less heating in the cables (P = I²R); so less energy is wasted. Write all three.
AP Physics and NGSS: AP Physics 1 does not cover transformers. NGSS HS-PS3-3 uses the grid as an example of designing a system that converts and transfers energy efficiently.
Written in Physiworld's own words. The course tags come from the same mapping as the syllabus maps; equations are on the IGCSE, GCSE, AP Physics 1 and NGSS formula sheets. Values use g = 9.8 N/kg.
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