Electricity: Current, Potential Difference and Resistance

This guide covers Topic 9, Electricity, in full — subtopics 9.1 Electric current, 9.2 Potential difference and power and 9.3 Resistance and resistivity — from Cambridge International AS & A Level Physics 9702, 2025–2027 series. This is AS Level content and starts a new strand of the course (electricity), building on IGCSE/O Level circuit basics.

Before studying this

A basic IGCSE/O Level understanding of current, voltage and simple circuits is assumed. This topic formalises those ideas with precise definitions and equations.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 — AS Level, Topic 9

9.1 Electric current — current as a flow of charge carriers; charge on charge carriers is quantised; recalling and using Q = It; using I = Anvq for a current-carrying conductor, where n is charge-carrier number density.

9.2 Potential difference and power — defining potential difference as energy transferred per unit charge; recalling and using V = W/Q; recalling and using P = VI, P = I²R and P = V²/R.

9.3 Resistance and resistivity — defining resistance; recalling and using V = IR; sketching I–V characteristics of a metallic conductor at constant temperature, a semiconductor diode and a filament lamp; explaining that a filament lamp’s resistance increases with current because its temperature increases; stating Ohm’s law; recalling and using R = ρL/A; understanding that an LDR’s resistance decreases as light intensity increases, and a thermistor’s resistance decreases as temperature increases (negative temperature coefficient assumed).

Electric current

Electric current is the rate of flow of charge, carried by charge carriers (electrons in a metal). Charge is quantised — it exists only in multiples of the elementary charge. The defining relationship:

Q = It

For a current-carrying conductor, current relates to the microscopic behaviour of charge carriers via:

I = Anvq

where A is cross-sectional area, n is the number density of charge carriers, v is their mean drift velocity, and q is the charge per carrier.

Typical drift velocities are tiny — millimetres per second — because metals have an enormous charge-carrier number density n, so for a given current only a very small v is needed to satisfy I = Anvq. This is why a lamp appears to switch on instantly even though individual electrons barely move: it is the electric field, not the electrons themselves, that propagates through the conductor at close to the speed of light, setting every free electron drifting almost simultaneously.

Potential difference and power

Potential difference (p.d.) across a component is the energy transferred per unit charge passing through it:

V = W/Q

Electrical power delivered to (or by) a component can be expressed three equivalent ways, depending on which quantities are known:

P = VI       P = I²R       P = V²/R

Resistance and resistivity

Resistance is defined by:

V = IR

Ohm’s law states that current through a conductor is proportional to the potential difference across it, provided physical conditions (notably temperature) stay constant.

I–V characteristics:

• A metallic conductor at constant temperature gives a straight line through the origin — it obeys Ohm’s law.
• A filament lamp curves, with the gradient decreasing as current increases — resistance increases with current because the filament heats up and its temperature rises, increasing resistance. This is a non-ohmic behaviour caused by temperature change, not a failure of V = IR itself.
• A semiconductor diode conducts easily in one direction (forward bias, low resistance once past a threshold voltage) and barely at all in the other (reverse bias, very high resistance).

Resistivity relates a material’s resistance to its dimensions:

R = ρL/A

where L is length, A is cross-sectional area, and ρ (resistivity) is a property of the material itself, independent of its shape. Because area is proportional to the square of diameter, doubling a wire’s diameter quarters its resistance (four times the area, for the same length) even though resistivity itself is unchanged — resistivity depends only on the material, never on the dimensions of a particular sample of it.

Worked example. A wire of resistivity 1.7 × 10⁻⁸ Ω m, length 2.0 m and cross-sectional area 5.0 × 10⁻⁷ m² has resistance:

R = ρL/A = (1.7 × 10⁻⁸ × 2.0) / (5.0 × 10⁻⁷) = 0.068 Ω

Temperature-dependent components. A light-dependent resistor (LDR) decreases in resistance as light intensity increases. A thermistor (assumed negative temperature coefficient at this level) decreases in resistance as temperature increases — the opposite behaviour to a metallic conductor, whose resistance increases with temperature.

Common mistakes

• Assuming every component obeys Ohm’s law. Filament lamps and diodes explicitly do not, over at least part of their I–V characteristic — sketching a straight line through the origin for either is a common error.
• Confusing resistivity (a material property, ρ) with resistance (a component property depending on dimensions, R) — resistivity does not change if you cut a wire in half; resistance does.
• Getting the LDR/thermistor resistance-temperature or resistance-light relationships backwards — both decrease resistance as the relevant condition (light or temperature) increases.
• Using P = VI when only current and resistance are known (or vice versa) — choose the power formula that matches the quantities actually given.

Quick revision checklist

• Q = It and I = Anvq
• V = W/Q, and the three equivalent power formulas
• V = IR and Ohm’s law, stated precisely
• I–V characteristics for a metallic conductor, diode and filament lamp
• R = ρL/A, distinguishing resistivity from resistance
• LDR and thermistor resistance behaviour

Related resources

• Superposition: Stationary Waves, Diffraction and Interference — the previous AS topic
• D.C. Circuits: Kirchhoff’s Laws and Potential Dividers — the next AS topic, applying these definitions to full circuits
• Cambridge AS & A Level Physics hub

Written against Cambridge International AS & A Level Physics 9702, 2025–2027 series. Always check the current syllabus for your examination year.