2 Electricity

A quantity symbol and its unit symbol can differ: current is represented by $I$ but measured in amperes, $A$; resistance is represented by $R$ but measured in ohms, $\Omega$. The value $0.25\,A$ therefore means a current of 0.25 amperes.

For an earthed metal-cased appliance: if the live wire touches the case, the earth wire provides a low-resistance path. A large fault current then flows and the fuse melts or circuit breaker trips, disconnecting the live supply and reducing the risk of electric shock.

A heating element is designed to use this effect. It becomes hot and transfers energy to its surroundings: a kettle heats water, a toaster heats bread, an electric heater warms a room, and an iron heats its soleplate.

Example: a 2.8 kW toaster operates at 230 V. First convert $2.8 kW = 2800 W$. Then $I = P/V = 2800/230 = 12.2 A$. From 3 A, 5 A, 10 A and 13 A fuses, choose 13 A: it is the smallest available rating above the normal operating current.

Example: a device draws 2.0 A from a 12 V supply for 30 s. $E = IVt = 2.0 × 12 × 30 = 720 J$. If time is given in minutes or hours, convert it to seconds before using SI units.

Domestic lights are connected in parallel. Each lamp receives the mains voltage, each branch can be switched independently, and one failed lamp does not break the paths through the other lamps.

The nature of a component matters because its resistance may not stay constant. For example, a filament lamp becomes hotter as current rises, so its resistance changes; the current is therefore set by the behaviour of the whole series circuit, not just by the number of components.

Use a variable power supply or a variable resistor to change the voltage. Record paired ammeter and voltmeter readings over a safe range, switch off between readings when temperature must be controlled, and repeat readings. Reverse the supply to obtain negative-voltage data, then plot voltage on the x-axis and current on the y-axis.

A longer connecting cable has a greater resistance than a similar short cable. With the same supply voltage, the charging current is smaller, so transferring the same charge takes longer.

The reverse changes also apply: in dimmer light an LDR has greater resistance, and at lower temperature the thermistor has greater resistance. These relationships are generally non-linear, so equal changes in light or temperature do not have to produce equal resistance changes.

Placed in an appropriate part of a circuit, the indicator can show that the path is complete or that a protected section is still carrying current.

Example: a 73 $\Omega$ resistor carries 7.8 mA. Convert $7.8 mA = 0.0078 A$, then $V = IR = 0.0078 \times 73 = 0.57 V$ to two significant figures.

A current of 3 A means that 3 coulombs of charge pass the point every second. If the rate is larger, more charge passes each second.

Example: a lamp carries 0.48 A for 30 s. $Q = It = 0.48 \times 30 = 14.4 C$, so about 14 C is transferred to two significant figures.

A metal contains positive ions fixed in a lattice and electrons that can move through the structure. When a voltage is applied, these mobile electrons gain a net drift through the metal, so charge is transferred along the conductor.

Current is a rate of charge flow. Charge is conserved, so in a steady circuit charge does not continually build up or disappear at the junction; the incoming flow rate must equal the combined outgoing flow rates.

Example: 0.60 A enters a junction. If one branch carries 0.20 A, the other carries $0.60 - 0.20 = 0.40 A$. The check is $0.20 + 0.40 = 0.60 A$.

Each branch begins and ends at the same pair of electrical points. A unit of charge therefore undergoes the same energy change between those points, whichever branch it follows.

If two resistors are each connected directly across a 4.5 V cell, the voltage across each resistor is 4.5 V. The currents in the two branches may still be different because their resistances may differ.

Example: 200 $\Omega$ and 400 $\Omega$ resistors are connected in series across 12 V. $R_{total}=600 \Omega$, so $I=V/R=12/600=0.020 A$. Then $V_1=IR_1=0.020 \times 200=4.0 V$ and $V_2=0.020 \times 400=8.0 V$.

Check both conservation rules: the same 0.020 A is used for each resistor, and $4.0 + 8.0 = 12 V$. The larger resistance receives the larger share of voltage in this series circuit.

A voltage of 6 V means that 6 joules of energy are transferred for every coulomb of charge that passes between the two points. If 2 C passes, the energy transferred is 12 J.

Example: 3.7 J is transferred when 4.3 mC passes. Convert $4.3 mC = 0.0043 C$, then $V=E/Q=3.7/0.0043=860 V$ to two significant figures.

Conductors are used when charge must flow, such as copper connecting wires. Insulators are used to prevent charge flow, such as plastic wire coverings. An insulating object can also keep electrostatic charge localised on its surface.

Use rods of equal dimensions made from different insulating materials. Discharge each rod before testing, then rub it with the same cloth using the same force, number of strokes and contact length. Bring the rod to the same distance from a suspended charged ball, an electroscope, or a charge meter and record the force, deflection, or charge reading. Repeat and compare mean results.

When two initially neutral insulators are rubbed, electrons can move from one surface to the other. The object that gains those electrons becomes negative; the object that loses the same electrons becomes positive. Charge is transferred, not created from nothing.

Two negatively charged droplets spread apart because each repels the other. A positive ball moves towards a negative rod because the unlike charges attract. The force acts along the line joining the charged objects and becomes weaker as their separation increases.

Example: negatively charged plastic wrapping is brought near a neutral plate. Its excess electrons repel electrons in the plate away from the nearby surface. That surface is left relatively positive, so the opposite charges close together attract and the wrapping sticks.

A positively charged object produces the reverse electron movement: electrons in the neutral object are attracted towards the near side. In either case, the attractive force from the closer unlike charges is stronger than the repulsion from the farther like charges.

During refuelling, fuel flowing through pipes can create separated charge. A spark near flammable fuel vapour can ignite it, causing fire or explosion. In a flour mill, a spark can ignite suspended combustible dust and cause an explosion.

In both devices, electrical control changes where charge remains or how a charged particle moves. The force is non-contact, so tiny droplets or toner particles can be positioned without a mechanical tool touching each one.