Unit 2: Electric Circuits

This guide covers sub-topic 2.4 Electric Circuits, completing Unit 2: Waves and Electricity, from the Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics (YPH11), Issue 3 specification (first assessment June 2019). This topic is commonly studied using applications such as space technology.

Before studying this

This topic follows sub-topic 2.3, Waves and Particle Nature of Light, and assumes familiarity with rearranging equations and basic circuit diagrams from GCSE/IGCSE-level physics.

Syllabus coverage

PEARSON EDEXCEL INTERNATIONAL A LEVEL PHYSICS (YPH11) — Sub-topic 2.4

Candidates will be assessed on their ability to: understand that electric current is the rate of flow of charged particles and use I = ΔQ/Δt; understand how to use the equation V = W/Q; understand that resistance is defined by R = V/I and that Ohm’s law is a special case when I ∝ V for constant temperature; understand how the distribution of current in a circuit is a consequence of charge conservation, and how the distribution of potential differences in a circuit is a consequence of energy conservation; derive the equations for combining resistances in series and parallel using the principles of charge and energy conservation, and use these equations; use the equations P = VI, W = VIt, and derive and use related equations such as P = I²R and P = V²/R; understand how to sketch, recognise and interpret current-potential difference graphs for components, including ohmic conductors, filament bulbs, thermistors and diodes; use the equation R = ρl/A; CORE PRACTICAL 7: determine the electrical resistivity of a material; use I = nqvA to explain the large range of resistivities of different materials; understand how the potential along a uniform current-carrying wire varies with distance along it; understand the principles of a potential divider circuit and how to calculate potential differences and resistances in such a circuit; analyse potential divider circuits where one resistance is variable, including thermistors and light dependent resistors (LDRs); know the definition of electromotive force (e.m.f.), understand internal resistance, and distinguish between e.m.f. and terminal potential difference; CORE PRACTICAL 8: determine the e.m.f. and internal resistance of an electrical cell; understand how changes of resistance with temperature may be modelled in terms of lattice vibrations and number of conduction electrons, and how to apply this model to metallic conductors and negative temperature coefficient thermistors; and understand how changes of resistance with illumination may be modelled in terms of the number of conduction electrons, and how to apply this model to LDRs.

Current, potential difference and resistance

Electric current is the rate of flow of charged particles:

I = ΔQ / Δt

Potential difference relates energy transferred to charge:

V = W / Q

Resistance is defined as R = V/I; Ohm’s law is the special case where current is proportional to potential difference at constant temperature (I ∝ V), giving a straight-line current-potential difference graph through the origin. Non-ohmic components — filament bulbs (curve as temperature rises), thermistors (current rises faster than linearly as resistance falls with heating) and diodes (near-zero current until a threshold forward voltage, then rapid rise; effectively no current in reverse) — have characteristic non-linear I-V graphs that must be sketched, recognised and interpreted.

Circuit laws and combining resistors

Current distribution in a circuit follows from conservation of charge (current into a junction equals current out); potential difference distribution follows from conservation of energy (energy transferred per unit charge around any closed loop sums to zero). From these principles, resistances combine as:

series:   R = R1 + R2 + R3 + ...
parallel: 1/R = 1/R1 + 1/R2 + 1/R3 + ...

Power in a circuit is P = VI, and energy transferred is W = VIt; combined with V = IR these give the related forms P = I²R and P = V²/R.

Resistivity and CORE PRACTICALs 7-8

Resistivity relates a material’s resistance to its dimensions:

R = ρl / A

where l is length and A is cross-sectional area — investigated in CORE PRACTICAL 7, determining the electrical resistivity of a material. At the microscopic level, current is described by I = nqvA, where n is the number density of charge carriers, q is charge per carrier, v is mean drift velocity and A is cross-sectional area — explaining why different materials (metals, semiconductors, insulators) span such a large range of resistivities. Along a uniform current-carrying wire, potential varies linearly with distance from one end.

A potential divider circuit splits a supply voltage across two or more resistors in series, in proportion to their resistances; when one resistance is variable — a thermistor or light dependent resistor (LDR) — the output potential difference varies with temperature or light level respectively, and candidates must be able to analyse such circuits.

Electromotive force (e.m.f.) is the total energy supplied per unit charge by a source; internal resistance is the resistance within the source itself, meaning the terminal potential difference (measured across the source’s terminals when current flows) is less than the e.m.f. by the “lost volts” across the internal resistance. CORE PRACTICAL 8 determines the e.m.f. and internal resistance of an electrical cell, typically from a graph of terminal potential difference against current.

Modelling resistance changes

Resistance changes with temperature can be modelled in terms of lattice vibrations (which increase and impede electron flow as temperature rises) and the number of conduction electrons (which, for negative temperature coefficient thermistors, increases sharply with temperature, dominating over increased lattice vibration and causing resistance to fall). This model applies to both metallic conductors (resistance rises with temperature, dominated by lattice vibrations) and NTC thermistors (resistance falls with temperature, dominated by increasing conduction electrons). Resistance changes with illumination in an LDR are modelled similarly, in terms of the number of conduction electrons increasing as light intensity increases, reducing resistance.

Worked example. A cell of e.m.f. 6.0 V and internal resistance 0.50 Ω is connected to an external resistor of 5.5 Ω. Find (a) the current in the circuit, and (b) the terminal potential difference.

(a) Total resistance = 5.5 + 0.50 = 6.0 Ω. Current I = e.m.f. / total resistance = 6.0 / 6.0 = 1.0 A.

(b) Terminal p.d. = e.m.f. − (I × internal resistance) = 6.0 − (1.0 × 0.50) = 5.5 V (equal to the p.d. across the external resistor, as expected).

Common mistakes

Confusing e.m.f. (energy per unit charge supplied by the source) with terminal potential difference (what is actually measured externally) — they are only equal when no current flows or internal resistance is zero. Adding resistances in parallel directly instead of using the reciprocal relationship. Forgetting that Ohm’s law only describes a special case (constant temperature, I ∝ V) rather than a universal definition of resistance. Misreading non-ohmic I-V graphs, particularly assuming a diode conducts symmetrically in both directions.

Quick revision checklist

• Use I = ΔQ/Δt, V = W/Q and R = V/I, and state the condition for Ohm’s law to apply.
• Explain current and potential-difference distribution using charge and energy conservation.
• Derive and use the series and parallel resistor-combination equations.
• Use P = VI, W = VIt, P = I²R and P = V²/R.
• Sketch and interpret I-V graphs for ohmic conductors, filament bulbs, thermistors and diodes.
• Use R = ρl/A and describe CORE PRACTICAL 7 (resistivity).
• Use I = nqvA to explain the range of material resistivities.
• Analyse potential divider circuits, including with a thermistor or LDR.
• Distinguish e.m.f. from terminal potential difference and describe CORE PRACTICAL 8 (e.m.f. and internal resistance).
• Explain resistance changes with temperature (conductors, NTC thermistors) and illumination (LDRs) in terms of lattice vibrations and conduction-electron number.

Related resources

• Unit 2: Waves and Particle Nature of Light — the previous sub-topic
• Unit 4: Further Mechanics, Fields and Particles — the first International A2 unit (Unit 3, Practical Skills in Physics I, comes between this unit and Unit 4)
• Pearson Edexcel International A Level Physics hub

This guide is intended to support, not replace, engagement with the official Pearson Edexcel specification and your own teacher’s guidance. Always check the current version of the specification for authoritative detail.