§ 4.1 Simple phenomena of magnetism
Key ideas
- Like poles repel, unlike poles attract; forces act between magnets, and between magnets and magnetic materials, without contact.
- Induced magnetism: a magnetic material becomes a magnet while it sits in a magnetic field.
- Soft iron magnetises and demagnetises easily: temporary magnets and electromagnet cores. Steel keeps its magnetism: permanent magnets.
- A magnetic field is the region where a magnetic pole feels a force. Field lines run from N to S, never cross, and are closest together where the field is strongest (at the poles).
- Plot a field with a small compass or iron filings.
Fig. 1 · A bar magnet's field: lines leave the north pole, loop round, and enter the south pole; the crowding of lines near the poles shows the field is strongest there.
Watch out: attraction proves nothing, because a magnet attracts any unmagnetised iron. Only repulsion proves that an object is itself a magnet.
§ 4.2 Electrical quantities
Key ideas
- Charge is measured in coulombs. Rubbing transfers electrons only: the object that gains them becomes negative, the one that loses them positive. Like charges repel.
- Conductors let electrons flow (metals); insulators do not (plastics). Extended: an electric field is the region where a charge feels a force; field lines point away from positive and into negative.
- Current is the rate of flow of charge, in amperes, measured by an ammeter in series. Conventional current runs from + to − round the circuit, opposite to the electron flow.
- d.c. flows one way; a.c. reverses direction repeatedly.
- EMF is the work done per unit charge by the source; p.d. is the work done per unit charge across a component; both in volts (1 V = 1 J/C), measured by a voltmeter in parallel.
- Resistance R = V / I. For a wire, R is proportional to length and inversely proportional to cross-sectional area (Extended).
- I-V graphs: a resistor gives a straight line through the origin; a filament lamp's curve flattens because the hot filament's resistance rises; a diode conducts in one direction only.
- The kilowatt-hour is the energy a 1 kW appliance transfers in 1 hour; cost = kWh × price per unit.
Equations
I = Q / tcurrent = charge ÷ time (Extended)A
R = V / Iresistance = p.d. ÷ currentΩ
P = I Vpower = current × p.d.W
E = I V tenergy transferred = current × p.d. × timeJ
Fig. 2 · Three I-V characteristics: constant resistance gives a straight line; a heating filament bends the lamp's curve over; a diode passes current one way only.
Watch out: the ammeter goes in series (the current must pass through it) and the voltmeter in parallel across the component. Swapping them is a classic circuit-drawing error.
§ 4.3 Electric circuits
Key ideas
- Series: one loop; the current is the same at every point; the p.d.s across components add up to the supply p.d.
- Parallel: each branch gets the full supply p.d.; the branch currents add up to the supply current.
- The combined resistance of parallel resistors is less than the smallest branch resistance: every extra branch is an extra route for current.
- Parallel wiring lets components work independently at full brightness or power, which is why mains circuits use it.
- Extended: a potential divider splits the supply p.d. between two resistors in the ratio of their resistances; with an LDR or thermistor it makes light and temperature sensors.
Equations
R = R1 + R2resistors in series addΩ
1/R = 1/R1 + 1/R2two resistors in parallel (Extended)Ω
Fig. 3 · Series shares the p.d. and keeps one current; parallel shares the current and gives every branch the full p.d.
Watch out: adding a resistor in parallel lowers the total resistance, because it opens another route for current. Two 10 Ω resistors in parallel make 5 Ω, not 20 Ω.
§ 4.4 Electrical safety
Key ideas
- Hazards: damaged insulation exposing the live wire, overheating cables, damp conditions (water lowers the body's resistance), and overloaded plugs and sockets.
- A fuse melts and breaks the circuit when the current is too large; it sits in the live wire so the appliance is disconnected from the dangerous side.
- A circuit breaker does the fuse's job faster and can be reset.
- The earth wire gives fault current a low-resistance path so a metal case can never sit at mains voltage; the large fault current then blows the fuse.
Watch out: a fuse rated far above the appliance's normal current gives no protection. Choose the next standard rating just above the working current: a 3 A fuse for a 2.6 A lamp, not 13 A.
§ 4.5 Electromagnetic effects
Key ideas
- Electromagnetic induction: an EMF is induced when a conductor cuts field lines, or the field through a circuit changes. It grows with faster movement, a stronger magnet, and more turns; reversing the motion reverses it.
- An a.c. generator is a coil rotating in a field, connected through slip rings; its output alternates every half turn.
- A current creates a magnetic field; a solenoid's field looks like a bar magnet's. This is the basis of electromagnets, relays and loudspeakers.
- Motor effect: a current-carrying conductor in a magnetic field feels a force perpendicular to both the field and the current (Fleming's left-hand rule, Extended); reversing either one reverses the force.
- In a d.c. motor the split-ring commutator swaps the current direction every half turn so the coil keeps turning the same way; more turns, more current or a stronger field gives a bigger turning effect.
- A transformer is two coils on a soft-iron core: a.c. in the primary makes a changing field, inducing an a.c. EMF in the secondary. More secondary turns step the voltage up.
- Extended: the grid transmits at high voltage so the current is small and the I²R heating loss in the cables stays low.
Equations
Vp / Vs = Np / Nsvoltage ratio = turns ratio for a transformerno unit
Ip Vp = Is Vspower in = power out for a 100% efficient transformer (Extended)W
Fig. 4 · The motor effect: with the field running N to S and the current out of the page, the wire is pushed upwards; reverse the current or the field and the force flips.
Fig. 5 · A step-up transformer: the alternating field set up by the primary threads the soft-iron core, and the greater number of secondary turns induces a larger voltage.
Watch out: a transformer only works on a.c. A steady d.c. current makes a constant field, nothing changes through the secondary, and no EMF is induced.