Electricity and Magnetism

4.1 Simple magnetism and magnetic fields

Poles and forces

A magnet has two poles, a north pole (N) and a south pole (S).

• Unlike poles attract (N and S).
• Like poles repel (N and N, or S and S).
• A magnet also attracts magnetic materials: iron, steel, nickel and cobalt. Other materials, such as copper, aluminium, plastic and glass, are non-magnetic.

Induced magnetism

A piece of magnetic material becomes a magnet when it is placed near or touching a magnet. This is induced magnetism. The end nearest the magnet becomes the opposite pole, so the two attract. A nail held to a magnet picks up pins in this way. When the magnet is taken away, soft iron loses almost all of its magnetism.

Temporary and permanent magnets

Magnetic fields

A magnetic field is a region in which a magnetic pole experiences a force.

• The direction of the field at a point is the direction of the force on a north pole placed there. Field lines point away from N and towards S.
• Plotting the field. Place a plotting compass near a magnet, mark where the needle points, move the compass along and repeat. Joining the marks gives a field line. Iron filings sprinkled on paper over a magnet line up along the field lines. A compass needle points along the field, so it can be used to find the direction of the field.
• Pattern around a bar magnet. The field lines leave the N pole, curve round and enter the S pole, and never cross.
• Strength. The field is stronger where the lines are closer together, which is near the poles.

Uses of magnets

• Permanent magnets: compasses, fridge door catches, loudspeakers, electric motors.
• Electromagnets (a coil of wire with an iron core, magnetic only while a current flows): scrapyard cranes, relays, electric bells, circuit breakers.

4.2.1 Electrical charge

There are two kinds of electric charge, positive and negative. Charge is measured in coulombs (C).

Charging by friction. Rubbing two insulators together transfers electrons (negative charge) from one to the other. Protons do not move.

• A polythene rod rubbed with a cloth gains electrons and becomes negative. The cloth loses electrons and becomes positive.
• An acetate rod rubbed with a cloth loses electrons and becomes positive.
• A charged rod attracts small pieces of paper. Two negative rods repel, while a negative and a positive rod attract.

Electric fields

An electric field is a region in which an electric charge experiences a force. The direction of an electric field line at a point is the direction of the force on a positive charge there.

Conductors and insulators

• Conductors let charge flow through them. Examples are metals and graphite.
• Insulators do not. Examples are plastic, glass, rubber and dry air.

Experiment. Connect a cell, a lamp and two clips in a circuit. Touch the clips to the test material. If the lamp lights, the material is a conductor.

Electron model. In a metal, some electrons are free to move through the material, so a current can flow. In an insulator, all the electrons are held tightly by their atoms, so there are no free charges to carry a current.

4.2.2 Electrical current

$I = \frac{12}{4.0} = 3.0\ \text{A} \qquad Q = It = 2.0 \times 30 = 60\ \text{C}$

• In metals, a current is a flow of free electrons.
• Conventional current is taken to flow from the positive terminal to the negative terminal. The electrons flow the other way, from negative to positive.
• Direct current (d.c.) flows in one direction only. Alternating current (a.c.) keeps reversing direction.
• An ammeter measures current. It is connected in series with the component. Choose a range that is bigger than the expected current, then move to a smaller range for a more precise reading.

4.2.3 Electromotive force and potential difference

Both are measured in volts (V), and $1\ \text{V} = 1\ \text{J/C}$.

$E = \frac{36}{12} = 3.0\ \text{V}$

• A voltmeter measures p.d. It is connected in parallel across the component.
• Cells in series add their e.m.f.s: three $1.5\ \text{V}$ cells in series give $4.5\ \text{V}$.
• Identical cells in parallel give the e.m.f. of one cell.

4.2.4 Resistance

$R = \frac{6.0}{2.0} = 3.0\ \Omega$

Experiment to find a resistance. Connect the resistor in series with an ammeter and a variable resistor, and a voltmeter in parallel across the resistor. Change the variable resistor to get several pairs of readings of $V$ and $I$. Calculate $\frac{V}{I}$ each time and average them (or plot a graph of $V$ against $I$; the gradient is $R$).

Resistance of a wire. For a wire of the same material:

• the resistance is directly proportional to the length: twice as long, twice the resistance;
• the resistance is inversely proportional to the cross-sectional area: twice as thick, half the resistance.

Current–voltage graphs

An increase in temperature increases the resistance of a metal such as the filament of a lamp.

4.3.1 Circuit diagrams and circuit components

4.3.2 Series and parallel circuits

Series circuit (one path for the current):

• the current is the same at every point;
• the total p.d. across the components is the sum of the p.d.s across each.

Parallel circuit (more than one path):

• the currents entering a junction equal the currents leaving it (so the branch currents add up to the total current);
• the p.d. across each branch is the same as across the whole arrangement.

The total resistance of resistors in parallel is always less than the smallest resistor.

$R = 4.0 + 6.0 = 10\ \Omega \qquad I = \frac{12}{10} = 1.2\ \text{A}$

$V_{4\Omega} = 1.2 \times 4.0 = 4.8\ \text{V} \qquad V_{6\Omega} = 1.2 \times 6.0 = 7.2\ \text{V}$

The two p.d.s add up to $12\ \text{V}$.

$R = \frac{6.0 \times 3.0}{6.0 + 3.0} = \frac{18}{9} = 2.0\ \Omega$

Each resistor has $12\ \text{V}$ across it: $I_{6\Omega} = \dfrac{12}{6.0} = 2.0\ \text{A}$ and $I_{3\Omega} = \dfrac{12}{3.0} = 4.0\ \text{A}$. The total current is $2.0 + 4.0 = 6.0\ \text{A}$, which agrees with $\dfrac{12}{2.0} = 6.0\ \text{A}$.

4.3.3 Action and use of circuit components

• A thermistor (NTC type) has a resistance that falls as its temperature rises. It is used as a temperature sensor, for example in a fire alarm or a thermostat.
• A light-dependent resistor has a resistance that falls as the light gets brighter. It is used as a light sensor, for example to switch on street lights when it gets dark.

The potential divider

Two resistors in series across a supply share the supply voltage in the ratio of their resistances.

The total is $6.0\ \text{k}\Omega$, so

$V_1 = 12 \times \frac{2.0}{6.0} = 4.0\ \text{V} \qquad V_2 = 12 \times \frac{4.0}{6.0} = 8.0\ \text{V}$

Check: $\dfrac{R_1}{R_2} = 0.5$ and $\dfrac{V_1}{V_2} = 0.5$.

A variable potential divider uses a variable resistor with a sliding contact. Moving the contact changes the output p.d. smoothly from $0\ \text{V}$ up to the full supply voltage (for example in a volume control). If a thermistor or LDR is one of the two resistors, the output p.d. changes with temperature or light, so the circuit can act as an input sensor that switches something on or off.

4.4.1 Uses of electricity

Electricity is used for heating, lighting, charging batteries, and powering motors and electronic systems.

Lamps in a lighting circuit are connected in parallel. Each lamp has the full supply voltage and can be switched on and off independently, and if one lamp fails the others stay on.

$P = IV = 10 \times 230 = 2300\ \text{W} = 2.3\ \text{kW}$

$E = IVt = 2.0 \times 12 \times 5.0 = 120\ \text{J}$

The kilowatt-hour

The kilowatt-hour (kW h) is the energy used by a device of power $1\ \text{kW}$ running for $1\ \text{hour}$.

$\text{energy} = 3.0 \times 4.0 = 12\ \text{kW h} \qquad \text{cost} = 12 \times 15 = 180\ \text{cents}$

4.4.2 Electrical safety

Hazards

• Damaged insulation can expose live wires, so a person can get an electric shock.
• Overheating cables can start a fire. A cable heats up if the current is too large for it.
• Damp conditions are dangerous because water conducts electricity, so the resistance of the body falls and a larger, more dangerous current can flow.
• Overloading a plug, extension lead or socket by plugging in too many appliances draws a very large current, which overheats the wires.

The mains wiring

The switch, the fuse and the circuit breaker are always in the live wire. If they were in the neutral wire, the appliance would still be connected to the live wire when it is "off", so touching its inside could give a shock.

Fuses and trip switches

• A fuse is a thin wire that melts if the current gets too high, breaking the circuit. Choose a fuse with a rating just above the normal current of the appliance. A $2.3\ \text{kW}$ appliance on $230\ \text{V}$ draws $\dfrac{2300}{230} = 10\ \text{A}$, so a $13\ \text{A}$ fuse is suitable and a $3\ \text{A}$ fuse is not.
• A trip switch (circuit breaker) uses an electromagnet to open a switch when the current is too high. It does the same job as a fuse, but can be reset instead of being replaced.

Earthing and double insulation

If a loose live wire touches a metal case, an earthed case carries a large current to the ground. This blows the fuse (or trips the breaker), cutting off the supply before anyone gets a shock. If the case were not earthed, it would become live and could give a fatal shock.

An appliance with a plastic casing (double insulated) has no metal that can become live, so it does not need an earth wire. The outer casing of an appliance must therefore be either non-conducting (double insulated) or earthed.

4.5.1 Electromagnetic induction

When a conductor cuts magnetic field lines, an e.m.f. is induced in it. If there is a complete circuit, a current flows.

Experiment. Connect a coil to a sensitive meter. Push a bar magnet into the coil, and the meter flickers. Hold the magnet still inside the coil, and the reading falls to zero. Pull the magnet out, and the meter flickers the opposite way. An e.m.f. is induced only while the magnetic field in the coil is changing.

The induced e.m.f. is bigger when:

• the magnet is moved faster (the rate of change of the field, or the rate of cutting field lines, is greater);
• the magnet is stronger;
• the coil has more turns.

For example, when the N pole of a magnet is pushed into a coil, the end of the coil nearest it becomes a north pole, which repels the magnet. The person pushing has to do work, and this work is the source of the electrical energy. A magnet dropped down a copper tube falls slowly for the same reason.

4.5.2 The a.c. generator

A simple a.c. generator has a coil that is rotated between the poles of a permanent magnet (or a magnet that rotates inside a coil).

• The ends of the coil connect to slip rings. Brushes (carbon contacts) press against the slip rings and connect the coil to the external circuit.
• As the coil turns, its sides cut the field lines and an e.m.f. is induced.

The graph of e.m.f. against time is a repeating wave (a sine wave).

• The e.m.f. is zero when the plane of the coil is perpendicular to the field, because the sides of the coil are moving along the field lines and not cutting them.
• The e.m.f. is at a maximum (a peak or a trough) when the plane of the coil is parallel to the field, because the sides cut the field lines at the greatest rate. The sign changes each half turn, so the current alternates.

Turning the coil faster increases both the size of the e.m.f. and the frequency. More turns on the coil, or a stronger magnet, also increase the e.m.f.

4.5.3 Magnetic effect of a current

A current in a wire produces a magnetic field around it.

• Straight wire. The field lines are concentric circles around the wire. The field is stronger near the wire and when the current is bigger. Reversing the current reverses the direction of the field. The direction can be found with the right-hand grip rule: point the thumb along the conventional current and the fingers curl in the direction of the field.
• Solenoid (a long coil). The field inside is strong and uniform, and the field outside is the same as that of a bar magnet. The field is stronger with a bigger current, more turns and an iron core. Reversing the current swaps the poles.

Uses

• A relay. A small current through a coil magnetises an iron core, which pulls a lever (the armature) and closes the contacts of a second circuit that carries a large current. A relay lets a small, safe circuit switch a large current in another circuit.
• A loudspeaker. A coil is fixed to a paper cone and sits in the field of a permanent magnet. An alternating current from the amplifier makes the coil move in and out (see 4.5.4), which moves the cone and produces sound waves of the same frequency.

4.5.4 Forces on a current-carrying conductor

A wire carrying a current in a magnetic field experiences a force, at right angles to both the field and the current.

Experiment. Place a copper rod across two rails between the poles of a strong magnet and pass a current through it. The rod rolls along the rails. Reversing the current or reversing the field reverses the direction of the force. Reversing both brings the force back to its original direction.

Parallel conductors. Two parallel wires with currents in the same direction attract each other. Two with currents in opposite directions repel each other. This is because the field of one wire acts on the current in the other.

4.5.5 The d.c. motor

A coil carrying a current in a magnetic field has forces on its two sides that act in opposite directions, so the coil experiences a turning effect.

The turning effect is increased by increasing:

• the number of turns on the coil,
• the current,
• the strength of the magnetic field.

How a d.c. motor works.

1. The coil is between the poles of a permanent magnet and connected to a d.c. supply through brushes.
2. The forces on the sides of the coil make it turn.
3. Each half turn, the split-ring commutator swaps the connections to the coil, so the current in each side reverses and the forces keep turning the coil in the same direction.
4. The brushes press against the commutator and keep contact with it as it turns.

Without the commutator, the coil would swing up to the vertical position and then be pulled back.

4.5.6 The transformer

A transformer changes the size of an alternating voltage. It has two coils, the primary and the secondary, wound on a soft iron core.

1. An alternating current in the primary coil produces a changing magnetic field in the core.
2. The iron core carries this changing field through the secondary coil.
3. The changing field induces an alternating e.m.f. in the secondary coil.

A transformer works only with a.c., because a d.c. supply gives a steady field that does not change, so nothing is induced.

• A step-up transformer has more turns on the secondary than on the primary, and increases the voltage.
• A step-down transformer has fewer turns on the secondary, and decreases the voltage.

$V_s = V_p \times \frac{N_s}{N_p} = 230 \times \frac{50}{1000} = 11.5\ \text{V}$

It is a step-down transformer.

$V_s = 12 \times \frac{2400}{100} = 288\ \text{V}$

High-voltage transmission

Power stations send electricity along cables at a very high voltage (tens or hundreds of thousands of volts), and step-down transformers reduce it for homes.

The reason is that $P = IV$. For the same power, a higher voltage means a smaller current. Power is wasted in the cables as heat, and this loss depends on the current (it is larger when the current is larger). A smaller current means much less power is wasted.

$I = \frac{P}{V}: \qquad \frac{100\,000}{230} = 435\ \text{A} \qquad \frac{100\,000}{23\,000} = 4.35\ \text{A}$

The current is a hundred times smaller at the higher voltage.

4.6 Uses of an oscilloscope

An oscilloscope displays a graph of voltage against time for a signal, such as the output of a microphone or a generator. The spot moves across the screen at a steady speed set by the timebase, and moves up and down in step with the voltage.

• A d.c. signal shows as a flat horizontal line, above or below the centre depending on the sign.
• An a.c. signal shows as a wave.

Measuring the p.d. Multiply the number of vertical divisions by the Y-gain setting (volts per division).

Measuring a short time. Multiply the number of horizontal divisions by the timebase setting (seconds per division). The frequency is $f = \dfrac{1}{T}$.

$\text{peak-to-peak} = 4 \times 2.0 = 8.0\ \text{V}$

$T = 5 \times 2.0\ \text{ms} = 10\ \text{ms} = 0.010\ \text{s} \qquad f = \frac{1}{0.010} = 100\ \text{Hz}$