Electricity

Electrostatics, circuit rules, Ohm's law and the V–I behaviour of components, plus power and energy.

11 min read

Insulators can be charged by friction: rubbing transfers electrons between them. It is always electrons that move; the object that gains electrons becomes negative, the one that loses them positive. Charge is always conserved.

Like charges repel, unlike charges attract. A charged object attracts even a neutral one by induction, which is why dust sticks to a charged screen. Earthing lets excess charge flow safely away, preventing sparks; this matters when refuelling aircraft or in fuel pipes.

Two circuit diagrams: a series circuit with a cell and two resistors in one loop, and a parallel circuit with two resistors on separate branches. — Series: one path, current the same everywhere. Parallel: branches share the voltage, total resistance falls.

Current is the rate of flow of charge: $I = \frac{Q}{t}$ (amps). Direct current (dc) flows one way; alternating current (ac) reverses repeatedly. Conductors (metals) let charge flow; insulators do not.

In a series circuit the current is the same everywhere and the voltages add, so $R = R_{1} + R_{2}$ . In a parallel circuit each branch has the full voltage and the currents add, so the total resistance is less than the smallest branch resistance.

Worked example

A charge of $60 C$ flows through a lamp in $30 s$ . Find the current.

$I = \frac{Q}{t} = \frac{60}{30} = 2 A .$

Two V–I graphs: a straight line through the origin for an ohmic resistor, and an S-shaped curve for a filament lamp that flattens at higher voltage. — An ohmic resistor gives a straight line (constant R); a filament lamp curves as it heats up and its resistance rises.

Resistance $R = \frac{V}{I}$ (ohms). A fixed resistor at constant temperature is *ohmic*: its $V - I$ graph is a straight line. A filament lamp heats up as current rises, so its resistance increases and the graph curves.

Components to know: an NTC thermistor's resistance falls as temperature rises; an LDR's resistance falls as light intensity rises; an ideal diode lets current flow one way only.

Worked example

A resistor carries $0.5 A$ when connected to $6 V$ . Find its resistance.

$R = \frac{V}{I} = \frac{6}{0.5} = 12 Ω.$

Voltage is energy per unit charge: $V = \frac{E}{Q}$ . Power $P = I V = I^{2} R$ , and the energy transferred is $E = V I t$ .

Worked example

A $230 V$ heater draws $4 A$ . Find its power and the energy used in $60 s$ .

$P = I V = 230 \times 4 = 920 W$ . $E = V I t = 920 \times 60 = 55200 J .$

Exam tip

Three power forms come from combining $P = I V$ with $V = I R$ : $P = I V = I^{2} R = \frac{V ^{2}}{R}$ . Pick whichever uses the two quantities the question gives you.

Saying positive charge "flows" in electrostatics (only electrons move).
Thinking parallel resistors give a bigger total resistance (it is always smaller than the smallest).
Mixing up $I = Q / t$ with $V = E / Q$ .

Electricity

Electrostatics

Circuits & current

Resistance & V–I graphs

Voltage, power & energy

Common mistakes