Electricity and Magnetism: From Ohm's Law to Household Wiring

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Charge and current

Electric charge is positive or negative; like charges repel and unlike charges attract. Its SI unit is the coulomb, and one electron carries a charge of 1.6 x 10^-19 C. Materials are conductors (silver is the best, then copper and aluminium), insulators (rubber, glass, plastic, dry wood) or semiconductors (silicon, germanium). Current is the rate of flow of charge, I = Q/t, measured in amperes (1 A = 1 C/s) by an ammeter connected in series. By convention current flows from the positive to the negative terminal, opposite to the flow of electrons.

Potential difference and Ohm's law

Potential difference is the work done to move a unit charge between two points, V = W/Q, measured in volts (1 V = 1 J/C) by a voltmeter connected in parallel; a cell or battery maintains it. Georg Simon Ohm stated in 1827 that, at constant temperature, the current through a conductor is proportional to the potential difference across it: V = IR, where R is the resistance in ohms. An ammeter has very low resistance and a voltmeter very high resistance, so that neither disturbs the circuit.

Resistance and resistivity

A wire's resistance is R = ρL/A: it grows with length, falls with cross-sectional area, and depends on the material and the temperature. Resistivity (ρ, in ohm metre) is a property of the material. A wire stretched to twice its length has half the area and four times the resistance. Copper and aluminium, of low resistivity, make transmission wires; nichrome, an alloy of high resistivity that does not oxidise when red-hot, makes heating elements; tungsten, with its very high melting point, makes bulb filaments. The resistance of metals rises with temperature, while that of semiconductors falls.

Series and parallel circuits

In series the same current passes through each resistor and R = R1 + R2 + R3, more than the largest; one break stops the whole circuit. In parallel each branch has the same potential difference and 1/R = 1/R1 + 1/R2 + 1/R3, less than the smallest: two 4 ohm resistors give 8 ohm in series and 2 ohm in parallel. Houses are wired in parallel so that every appliance gets the full voltage and can be switched on and off independently.

Electric power and energy

Power is P = VI = I^2R = V^2/R, in watts. Energy is power multiplied by time, and its commercial unit is the kilowatt hour: 1 kWh = 1 unit = 3.6 x 10^6 J, so a 100 W bulb used for 10 hours consumes 1 unit. The heating effect of current follows Joule's law, H = I^2Rt, and is used in heaters, irons, kettles, bulbs and fuses.

Magnetism from current and the motor

In 1820 Hans Christian Oersted saw a current-carrying wire deflect a compass needle, showing that electricity produces magnetism. The right-hand thumb rule gives the direction of the magnetic field around a straight wire. A current-carrying coil (solenoid) acts like a bar magnet, and with a soft iron core it becomes an electromagnet, used in electric bells, relays and cranes that lift scrap iron. A current-carrying conductor in a magnetic field feels a force whose direction is given by Fleming's left-hand rule (forefinger field, middle finger current, thumb motion). This is the principle of the electric motor, which turns electrical energy into mechanical energy; a DC motor uses a split-ring commutator to reverse the current every half turn. Fans, mixers, pumps and washing machines run on motors.

Induction, generators and transformers

In 1831 Michael Faraday found that a changing magnetic field through a coil induces a current in it; this is electromagnetic induction, and Fleming's right-hand rule gives the direction of the current. A generator (dynamo) uses it to turn mechanical energy into electrical energy. A transformer works on mutual induction and only on AC: a step-up transformer, with more turns in the secondary coil, raises the voltage at power stations so that power can travel far with little loss, and a step-down transformer lowers it near homes. Alternating current reverses direction periodically; in India its frequency is 50 Hz, so it changes direction every 1/100 second. Cells and batteries give direct current, which flows one way. A rectifier changes AC to DC and an inverter DC to AC.

Household wiring and safety

Homes receive AC at about 220 to 230 V through a live wire, a neutral wire and an earth wire; NCERT gives their insulation colours as red, black and green, while many newer cables and appliance cords use the international code of brown (live), blue (neutral) and green with yellow stripes (earth). The earth wire connects the metal bodies of irons, refrigerators and toasters to the ground, so leaking current flows to earth instead of through the user. A fuse, a wire of low melting point placed in series with the live wire, melts when excess current flows because of a short circuit (live and neutral wires touching) or overloading (too many appliances on one socket); a miniature circuit breaker (MCB) does the same job and can simply be reset. Switches are always fitted in the live wire, and a bird sitting on a single wire is safe because there is no potential difference across its body.

Key facts

Charge on an electron = 1.6 x 10^-19 C; I = Q/t (ampere); ammeter in series (low resistance), voltmeter in parallel (high resistance).
Ohm's law (1827): V = IR at constant temperature; R = ρL/A, so a wire stretched to double its length has four times the resistance.
Heating elements: nichrome (high resistivity, does not oxidise); bulb filament: tungsten (very high melting point); transmission lines: copper and aluminium.
Series: same current, R = R1 + R2; parallel: same voltage, 1/R = 1/R1 + 1/R2; houses are wired in parallel.
P = VI = I^2R = V^2/R; 1 unit = 1 kWh = 3.6 x 10^6 J; a 100 W bulb used for 10 hours consumes 1 unit.
Oersted (1820): current produces magnetism; Faraday (1831): a changing magnetic field produces current (electromagnetic induction).
Fleming's left-hand rule: motor (electrical to mechanical energy); right-hand rule: generator (mechanical to electrical energy).
Transformer: mutual induction, works only on AC; step-up at the power station, step-down near homes; rectifier AC to DC, inverter DC to AC.
Indian mains: AC, 50 Hz, about 220-230 V; fuse in series with the live wire; the earth wire protects users from shocks through metal bodies; switches go in the live wire.

Quick revision

Electron charge 1.6 x 10^-19 C; ampere = coulomb per second; V = IR (Ohm, 1827); R = ρL/A; nichrome heaters, tungsten filament; series resistances add, parallel reciprocals add; houses wired in parallel; P = VI; 1 kWh = 3.6 x 10^6 J; Oersted 1820, Faraday 1831; left-hand rule motor, right-hand rule generator; transformer works only on AC; India 50 Hz AC; fuse in live wire, low melting point; earth wire against shocks.

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