Topic D: Electricity and Magnetism

Electricity and Magnetism is the largest compulsory part. It builds from static charge to current electricity, develops the rules for series and parallel circuits, covers safe use of mains electricity at home, then links electricity and magnetism through magnetic forces, the motor effect and electromagnetic induction, which underpins generators and transformers.

Electrostatics

Matter contains positive and negative electric charge, and like charges repel while unlike charges attract. An object becomes charged when electrons are transferred to or from it, for example by rubbing two insulators together; the object gaining electrons becomes negative and the one losing them positive. Charge is measured in coulombs. A charged object sets up an electric field in the space around it, and a small test charge placed in the field experiences a force; field lines point away from positive charge and toward negative charge. Everyday effects of static charge include attraction of small pieces of paper, sparks when discharging, and the need to earth fuel tankers to prevent dangerous sparks.

Current, voltage and resistance

Electric current is the rate of flow of charge, I = Q over t, measured in amperes; conventional current flows from positive to negative, opposite to the electron flow. Voltage, or potential difference, is the energy transferred per unit charge between two points, V = E over Q, measured in volts, and is what drives the current. Resistance opposes the flow of current and is defined as R = V over I, measured in ohms. A larger resistance allows less current for a given voltage. Resistance increases with the length of a wire, decreases with greater cross-sectional area, and depends on the material and its temperature; most metals increase in resistance when they get hotter.

Ohm's law and I-V characteristics

Ohm's law states that for a metallic conductor at constant temperature the current is directly proportional to the voltage across it, so V over I (the resistance) stays constant. Such a component is called ohmic and its current-voltage graph is a straight line through the origin. Many components are non-ohmic: a filament lamp curves because its resistance rises as the filament heats up, and a diode conducts in only one direction, giving a very high resistance in reverse. A thermistor's resistance falls as temperature rises, and a light-dependent resistor's resistance falls as light increases; both are useful in sensing circuits. Sketching and interpreting these characteristic graphs is a common DSE task.

Circuits and electrical energy and power

In a series circuit the same current flows through every component, the voltages add up to the supply voltage, and the total resistance is the sum of the individual resistances. In a parallel circuit each branch has the full supply voltage, the branch currents add up to the total, and the combined resistance is less than the smallest individual resistance. Electrical power is the rate at which energy is transferred, P = I V, which can be rewritten using Ohm's law as P = I squared R or P = V squared over R. The electrical energy used is E = P t = I V t, and domestic energy is billed in kilowatt-hours, where one kilowatt-hour is the energy used by a one kilowatt appliance in one hour.

Domestic electricity and safety

Mains electricity in Hong Kong is supplied at about 220 volts as alternating current. A three-pin plug carries live, neutral and earth wires; the live wire alternates in potential, the neutral stays near zero, and the earth wire connects the metal casing of an appliance to the ground for safety. A fuse or circuit breaker is placed in the live wire and breaks the circuit if the current becomes dangerously large, for example during a short circuit. Earthing prevents a metal case from becoming live: if a fault connects the live wire to the case, a large current flows to earth and blows the fuse, protecting the user. Double insulation is an alternative safety measure for appliances with plastic casings.

Magnetic fields and the motor effect

A magnet creates a magnetic field, a region where magnetic materials and moving charges feel a force, represented by field lines running from north to south pole. An electric current also produces a magnetic field: around a straight wire the field is circular, and a coil (solenoid) behaves like a bar magnet, the basis of the electromagnet. When a current-carrying wire lies in a magnetic field it experiences a force, the motor effect, whose direction is given by Fleming's left-hand rule and whose size increases with current, field strength and wire length. A coil carrying current in a field experiences a turning effect, which is how the direct-current electric motor spins.

Electromagnetic induction and transformers

Electromagnetic induction is the production of a voltage (and current, if the circuit is complete) whenever the magnetic flux linking a conductor changes, for example by moving a magnet into a coil. Faraday's law states that the induced voltage is larger when the flux changes faster or when there are more turns, and Lenz's law states that the induced current opposes the change that produced it, which is a consequence of energy conservation. A generator uses this effect to convert mechanical energy into electrical energy. A transformer uses a changing current in a primary coil to induce a voltage in a secondary coil on the same iron core; the voltage ratio equals the turns ratio, Vs over Vp = Ns over Np, allowing voltages to be stepped up for efficient power transmission and stepped down for safe use.