Electricity

A-Level Physics 9702 · Topic 9 revision notes · AS

Charge on the move: current and drift velocity, potential difference and power, resistance, I-V characteristics and resistivity.

11 definitions to learn word for word, 11 equations in their own column, 7 diagrams and graphs. Read it, cover it, test yourself.

Definitions (mark-scheme wording)EquationsExam traps

9.1Electric current

Electric current: the rate of flow of charge.
Coulomb: the charge passing a point when a current of one ampere flows for one second (1 C = 1 A s).
Elementary charge (e): the smallest free charge: the magnitude of the charge on an electron or proton, 1.60 × 10^-19 C.
Number density (n): the number of free charge carriers per unit volume.

Charge is quantised: any charge is a whole-number multiple of e.
Charge carriers: electrons in metals; ions (positive and negative) in electrolytes and ionised gases.
Conventional current flows from + to -, opposite to the electron flow.
Drift speed in a metal is very small (~10^-4 m s^-1) because n is huge.
Semiconductors have much smaller n, so for the same current the drift speed is much larger.
Same current through a thinner section: drift speed is larger (v = I/nAq).

I = Anvq: in one second, all carriers within a length v of the shaded face pass through it. Conventional current is opposite to the electron drift.

Same current I in series: where the wire is thinner (smaller A), the carriers must drift faster.

Use q = 1.60 × 10^-19 C for an electron in I = Anvq; the sign is ignored for the speed.
Current is not used up: it is the same at every point in a series loop.

Potential difference (p.d.): the energy transferred from electrical to other forms per unit charge.
Volt: one joule per coulomb (1 V = 1 J C^-1).
Power: the rate of energy transfer (work done per unit time).

P.d. is measured across a component with a voltmeter in parallel; current with an ammeter in series.
Ideal voltmeter: infinite resistance. Ideal ammeter: zero resistance.
Three power forms, linked by V = IR: pick the one using the quantities you know.
For a fixed resistor, P ∝ I²: doubling I quadruples the power dissipated.
Transmission: high voltage means low current, so cable losses (I²R) are small.

Measuring the power of a resistor: ammeter in series, voltmeter in parallel, then P = VI.

P = I²R and P = V²/R need the I or V of that component, not of the whole circuit.
Energy in joules needs time in seconds, not minutes or hours.

Resistance: the ratio of the potential difference across a component to the current in it (R = V/I).
Ohm: the resistance of a component with a p.d. of one volt across it when the current is one ampere (1 Ω = 1 V A^-1).
Ohm's law: for a metallic conductor at constant temperature, the current is directly proportional to the potential difference.

Resistance at a point on an I-V graph = V/I at that point, not the gradient.
Metallic conductor at constant temperature: straight line through the origin (ohmic).
Filament lamp: curve flattens. Larger current, higher temperature, more lattice vibration, so R increases.
Semiconductor diode: almost no current in reverse; conducts above about 0.6 V forward, then R falls sharply.
Thermistor (NTC): resistance decreases as temperature increases.
Light-dependent resistor (LDR): resistance decreases as light intensity increases.

I-V characteristics: metallic conductor at constant temperature (ohmic), filament lamp (R rises with current), diode (conducts one way only).

Sensing resistors: thermistor resistance falls as temperature rises; LDR resistance falls as light intensity rises.

A curved I-V graph does not mean R = 1/gradient. Use R = V/I read from the point.
On an I-V graph (I up, V across) a curve bending towards the V axis means resistance is increasing.

Resistivity (ρ): the resistance of a sample of the material of unit length and unit cross-sectional area; defined by ρ = RA/L.

Resistivity is a property of the material (and temperature); resistance depends also on the shape.
R ∝ L and R ∝ 1/A: double the length doubles R; double the diameter quarters R.
Experiment: measure diameter with a micrometer at several places; A = πd²/4.
Measure R for several lengths (V/I or ohmmeter); plot R against L: gradient = ρ/A.
Keep the current small so the wire does not heat up and change ρ.

Geometry sets the resistance: R is proportional to length and inversely proportional to cross-sectional area.

Finding resistivity: R against L is a straight line through the origin with gradient ρ/A, so ρ = gradient × A.

The unit of resistivity is Ω m, not Ω/m or Ω m^-1.
Use the radius in πr², or d in πd²/4; do not mix them. Convert mm to m first.