OCR A-Level Physics: Electricity and Circuits

Electricity and circuits is the second great pillar of H556 Paper 1, sitting alongside mechanics as a co-equal source of marks across the modelling-physics examination. The module is conceptually deep but procedurally routine: every problem reduces to applying a small toolkit of laws — Ohm's law, Kirchhoff's two laws, the resistance combination rules, and the potential-divider relation — to a circuit diagram. The candidate who internalises this toolkit and applies it with discipline can solve almost every standard A-Level circuit item; the candidate who reaches for V = IR without first identifying which V and which I apply to which component will lose marks consistently throughout Paper 1.

H556 examiners weight this material heavily because circuit analysis is the gateway to almost everything later: capacitors in Capacitors and Fields depend on time-constant RC analysis, electromagnetic induction depends on Kirchhoff's voltage law applied to time-varying EMFs, and the photoelectric effect in Quantum Physics is read off a circuit-style stopping-potential measurement. A candidate who is confident with Kirchhoff's loops can extend the same logic into AC, RC, RL and RLC circuits at undergraduate level; a candidate who is uncertain about which sign convention applies on which loop will struggle on every multi-loop circuit question.

Course 4 of the H556 Physics learning path on LearningBro, Electricity and Circuits, develops the circuit-analysis vocabulary the rest of the path will use. It opens with electric current as charge flow and develops mean drift velocity as the microscopic picture (I = nAvq), moves through Kirchhoff's first law (charge conservation at a junction) and EMF / potential difference as energy-per-charge quantities, builds up resistance and Ohm's law, surveys the I-V characteristics of ohmic and non-ohmic components, develops resistivity as a material property and electrical power as a quantitative outcome, introduces internal resistance and the terminal-pd / EMF distinction, then layers in series and parallel combination rules, Kirchhoff's second law (energy conservation around a loop), and closes with the potential-divider circuit as the practical sensor interface. It sits between Newton's Laws and Momentum and Waves and Optics in the LearningBro OCR A-Level Physics learning path, bridging the mechanical and electromagnetic halves of the H556 specification.

Guide Overview

The Electricity and Circuits course is built as a twelve-lesson sequence that moves from the microscopic picture of current through component characteristics into multi-loop circuit analysis. The progression deliberately develops the conservation laws (Kirchhoff's first and second laws) at separate stages rather than as a single block, so the candidate can absorb each law in its own context before combining them.

• Electric Current and Charge
• Mean Drift Velocity
• Kirchhoff's First Law
• EMF and Potential Difference
• Resistance and Ohm's Law
• I-V Characteristics
• Resistivity
• Electrical Power and Energy
• Internal Resistance and EMF
• Series and Parallel Circuits
• Kirchhoff's Second Law
• Potential Dividers

OCR H556 Specification Coverage

This course addresses OCR H556 Module 4.1 (Charge and current), Module 4.2 (Energy, power and resistance) and Module 4.3 (Electrical circuits) in full. The specification organises the topic into the microscopic picture of current, energy and power, resistivity, internal resistance, Kirchhoff's laws, series/parallel combinations and the potential divider (refer to the official OCR specification document for exact wording).

• Module 4.1.1 — Current as charge flow; Kirchhoff's first law (lessons: electric-current-and-charge, mean-drift-velocity, kirchhoffs-first-law)
• Module 4.2.1 — Potential difference and EMF (lessons: emf-and-potential-difference)
• Module 4.2.2 — Resistance, Ohm's law and I-V characteristics (lessons: resistance-and-ohms-law, iv-characteristics)
• Module 4.2.3 — Resistivity (lessons: resistivity)
• Module 4.2.4 — Power and energy (lessons: electrical-power-and-energy)
• Module 4.2.5 — Internal resistance (lessons: internal-resistance-and-emf)
• Module 4.3.1 — Series and parallel; Kirchhoff's second law (lessons: series-and-parallel-circuits, kirchhoffs-second-law)
• Module 4.3.2 — Potential divider (lessons: potential-dividers)

Module 4 is examined predominantly on Paper 1 (Modelling physics) for the standard circuit-analysis items, with Paper 3 (Unified physics) deploying the same techniques against sensor-circuit and measurement-instrument scenarios.

Topic-by-Topic Walkthrough

Electric Current, Charge and Drift Velocity

The electric current and charge lesson defines current as the rate of flow of charge, I = ΔQ/Δt, measured in amperes (1 A = 1 C s⁻¹) and develops the convention that current flows from positive to negative terminal externally, while electrons (the actual charge carriers in a metal) drift from negative to positive. The elementary charge e = 1.6 × 10⁻¹⁹ C is the quantum of charge for the purposes of A-Level. The mean drift velocity lesson develops the microscopic picture: I = nAvq where n is the number density of free charge carriers, A is the cross-sectional area, v is the mean drift velocity, and q is the charge per carrier. A standard worked example: a copper wire of cross-section 1.0 × 10⁻⁶ m² carrying 1.0 A with n = 8.5 × 10²⁸ m⁻³ free electrons has v = I/(nAq) = 1.0 / (8.5 × 10²⁸ × 1.0 × 10⁻⁶ × 1.6 × 10⁻¹⁹) ≈ 7.4 × 10⁻⁵ m s⁻¹ — a remarkably slow drift, yet the signal propagates at near-light-speed because the electric field establishes itself almost instantaneously throughout the wire.

Kirchhoff's First Law and EMF / Potential Difference

The Kirchhoff's first law lesson develops the law as conservation of charge at a junction: the sum of currents flowing into a junction equals the sum flowing out. The EMF and potential difference lesson develops the critical distinction. EMF (electromotive force) is the energy delivered per unit charge by a source — chemical in a battery, mechanical in a generator, light in a photocell — measured in volts (J C⁻¹). Potential difference is the energy converted from electrical to other forms per unit charge across a component, also measured in volts. The two are conceptually different but dimensionally identical, and the routine A-Level error is to use them interchangeably without the underlying distinction. The Top-band discriminator is the explicit identification of EMF as the source's input to the circuit and pd as the component's output from the circuit.

Resistance, Ohm's Law and I-V Characteristics

The resistance and Ohm's law lesson defines resistance as R = V/I (always — this is the definition) with the ohm (V A⁻¹) as the SI unit. Ohm's law is the empirical observation that for some components, R is constant over a range of pd — these components are called ohmic, and the I-V characteristic is a straight line through the origin. The I-V characteristics lesson surveys the four canonical components: a metallic conductor at constant temperature (ohmic, straight line), a filament lamp (non-ohmic, curves over because R increases with temperature), a diode (non-ohmic, conducts in one direction only with a threshold around 0.7 V), and a thermistor (NTC type — resistance decreases with temperature, giving a non-linear I-V). The Top-band discriminator is the explanation: a filament lamp's resistance increases with temperature because electron-lattice collisions increase, while a thermistor's resistance decreases with temperature because more charge carriers are released by thermal excitation in the semiconductor.

Resistivity and Electrical Power

The resistivity lesson develops R = ρL/A where ρ is the resistivity (a material property in Ω m), L is the length and A is the cross-sectional area. The PAG measurement of resistivity by plotting R against L/A and extracting ρ from the gradient is the standard practical-endorsement task. Copper has resistivity around 1.7 × 10⁻⁸ Ω m, nichrome around 1.1 × 10⁻⁶ Ω m, glass around 10¹² Ω m — the seventeen-order-of-magnitude range across materials is the qualitative basis for the conductor / semiconductor / insulator classification. The electrical power and energy lesson develops P = VI in its most general form, with P = I²R (preferred when current is known) and P = V²/R (preferred when pd is known) as algebraic specialisations. Energy transferred is E = Pt, with the kilowatt-hour (3.6 × 10⁶ J) as the practical billing unit.

Internal Resistance and EMF

The internal resistance lesson develops the real-cell model: an ideal EMF source ε in series with an internal resistance r. When the cell drives current I through an external circuit, the terminal pd V (the voltage measured across the cell's terminals) is V = ε − Ir, less than the EMF by the 'lost volts' Ir dissipated inside the cell. The PAG measurement plots V against I (varying the external load) and extracts ε from the y-intercept and r from the (negative) gradient. The Top-band discriminator is the recognition that the maximum power transferred to an external load occurs when the external resistance equals the internal resistance (the impedance-matching condition), and that this maximum-power condition has only 50% efficiency because half the power is dissipated inside the cell.

Series, Parallel, Kirchhoff's Second Law and Potential Dividers

The series and parallel circuits lesson develops the combination rules. In series, the same current flows through every component, the pds add, and resistances add (R_total = R₁ + R₂ + ...). In parallel, the same pd is across every component, the currents add, and reciprocal resistances add (1/R_total = 1/R₁ + 1/R₂ + ...). The Kirchhoff's second law lesson develops the law as conservation of energy around any closed loop: the sum of EMFs around the loop equals the sum of pd drops, with consistent sign convention (traverse the loop in one direction and count EMF rises as positive, pd drops as positive when traversed in the direction of conventional current). The potential dividers lesson develops the divider equation V_out = V_in × R₂/(R₁ + R₂) and the sensor-interface application: a thermistor or LDR in one arm of the divider produces a temperature- or light-dependent output voltage that can drive a downstream amplifier or analogue-to-digital converter.

A Typical H556 Paper 1 Question

A standard Paper 1 prompt gives candidates a multi-loop circuit — typically two cells of stated EMF and internal resistance with a network of three or four external resistors — and asks them to compute the current in each branch, the pd across a stated component, and the power dissipated in a stated resistor. The route is fixed. Label every branch current with a chosen direction (guessing the direction is fine — a negative answer just means the actual current flows the other way). Apply Kirchhoff's first law at each junction. Apply Kirchhoff's second law around each independent loop. Solve the resulting simultaneous equations. Compute the pd and power from the branch currents. The mark profile splits roughly AO1 (statement of the two Kirchhoff laws and the resistance combination rules) 3 marks, AO2 (substitution and solution of the simultaneous equations) 6 marks, AO3 (evaluation of physical reasonableness — current direction, power dissipation comparable to source delivery) 3 marks. The Top-band discriminator is the explicit sign convention declared at the outset and maintained through every equation, plus the energy-balance check at the end (total power delivered by the EMFs equals the total power dissipated in all resistances, including internal).

Synoptic Links

Electricity and circuits thread synoptically through almost every later H556 module. The same Kirchhoff's law framework reappears in Capacitors and Fields when RC time-constant analysis is developed (V_C = V_0(1 − e^(−t/RC)) during charging, V_C = V_0 e^(−t/RC) during discharging), and the resistor-capacitor sign convention is the direct extension of the resistor-only sign convention learned here. The potential-divider concept is the prerequisite for the photoelectric stopping-potential measurement in Quantum Physics, where the stopping voltage applied across a vacuum photocell can be analysed as a divider against a calibrated resistor.

Internal resistance and the EMF distinction reappear in Astrophysics and Cosmology when stellar luminosity is computed as a black-body 'EMF' source delivering power to the external universe with characteristic spectral signature, and in Nuclear and Particle Physics when ionisation chambers and Geiger-Müller tubes are analysed as circuit elements with characteristic plateau and burnout regions. The mean drift velocity calculation underpins the analysis of cyclotron and bubble-chamber tracks where the macroscopic current is interpreted in terms of microscopic charge-carrier behaviour.

Paper 3 'Unified physics' items typically deploy this module against unfamiliar contexts. A sensor-engineering scenario might give a Wheatstone-bridge circuit with a strain-gauge in one arm and ask candidates to derive the output voltage as a function of the strain. A medical-physics scenario might give an ECG amplifier circuit and ask candidates to identify the input impedance from a potential-divider analysis. An automotive scenario might give the charging-circuit topology of an alternator with internal resistance and ask candidates to predict the terminal pd at different load currents. In every case the underlying skill is the circuit-analysis fluency built in this module.

What Examiners Reward

Top-band marks on this module cluster around explicit sign-convention discipline and consistent application of the Kirchhoff laws. For multi-loop problems, examiners want every current labelled with a direction on the circuit diagram, every traversal direction declared for each loop, and every EMF and pd entered with the correct sign relative to that traversal direction. For resistor-combination problems, they want explicit identification of series and parallel sub-circuits with the combination rules stated. For internal-resistance problems, they want the explicit distinction between EMF (constant property of the cell) and terminal pd (varies with load current). For power-dissipation problems, they want the choice of P = I²R or P = V²/R justified by which quantity (I or V) is given directly.

Common pitfalls cluster around six recurring mistakes. First, using V = IR with mismatched V and I — for example, the total V across a series chain divided by the current through one resistor gives a fictitious 'total resistance' that is not the same as the sum of resistances. Second, treating EMF as identical to terminal pd, forgetting the internal resistance correction Ir. Third, applying the parallel combination rule directly to the resistances themselves (R_par = R₁ + R₂) instead of to the reciprocals. Fourth, omitting the sign convention in Kirchhoff's second law, leading to one equation with the wrong sign and an inconsistent simultaneous system. Fifth, computing power from P = V²/R using the EMF of the source rather than the pd across the specific resistor whose power is being computed. Sixth, using cross-sectional area in mm² in the resistivity formula R = ρL/A instead of m², giving resistance out by a factor of 10⁶. Each of these is a one- or two-mark deduction that compounds across a multi-part question.

Practical Activity Groups (PAGs)

This course anchors three OCR H556 PAGs in full. PAG 4 (Investigation of the I-V characteristics of components) uses a variable resistor or potential divider to sweep the pd across a filament lamp, diode and resistor and plot the I-V curves, audited explicitly for the discrimination between ohmic and non-ohmic behaviour. PAG 5 (Investigation of resistivity) measures R against L for a uniform wire (typically nichrome) at constant cross-section and extracts ρ from the gradient × A; the uncertainty propagation from Foundations and Measurement is heavily audited because the cross-sectional area carries a substantial percentage uncertainty when measured with a micrometer. PAG 4 (also internal resistance) plots terminal pd against current for a cell delivering current to a variable external load and extracts EMF (y-intercept) and internal resistance (negative gradient). The practical-endorsement column of the H556 record specifically demands evidence of circuit-diagram-to-physical-build translation skill, so this module's content is examined by both the written papers and the school-internal practical-endorsement assessment.

Going Further

Undergraduate analogues of this material extend in three directions. First, Kirchhoff's laws generalise into the linear-algebra framework of mesh analysis and nodal analysis, where multi-loop circuits are solved by matrix inversion rather than by hand-substitution into simultaneous equations. Second, resistivity generalises into the band theory of solids, where the seventeen-order-of-magnitude range between copper and glass is explained by the energy gap between the valence and conduction bands in different materials, leading naturally into the physics of semiconductors and the p-n junction diode. Third, the Ohm's-law I-V linearity generalises into the impedance concept for AC circuits, where capacitors and inductors contribute reactance terms 1/(jωC) and jωL that depend on frequency, and the steady-state circuit equations become complex-valued algebraic equations rather than time-dependent differential equations. Oxbridge-style interview prompts on this material include: "Why does a filament lamp's resistance increase with temperature while a thermistor's decreases?" "If you connect three identical resistors in parallel, what is the resistance of the combination, and why is it intuitively less than any individual resistor?" "A car battery has EMF 12 V and internal resistance 0.05 Ω; what is the maximum power it can deliver to an external load, and what load resistance achieves it?"

The Core Equations, Set Out Cleanly

Circuit analysis rests on a compact toolkit. Almost every Module 4 question is one of these relationships applied with discipline to a diagram.

Charge and current. Current as rate of charge flow, and the microscopic drift picture:

$I = \dfrac{\Delta Q}{\Delta t} \qquad I = nAvq$I=ΔtΔQ​I=nAvq

Resistance, Ohm's law and resistivity. The definition of resistance (always true), Ohm's law (true only for ohmic components), and the material relationship:

$R = \dfrac{V}{I} \qquad V = IR \quad (\text{ohmic}) \qquad R = \dfrac{\rho L}{A}$R=IV​V=IR(ohmic)R=AρL​

Power and energy:

$P = VI = I^2 R = \dfrac{V^2}{R} \qquad E = Pt$P=VI=I2R=RV2​E=Pt

Internal resistance. The real-cell model with EMF $\varepsilon$ε, internal resistance $r$r, and terminal pd $V$V:

$\varepsilon = I(R + r) \qquad V = \varepsilon - Ir$ε=I(R+r)V=ε−Ir

Combination rules and the potential divider:

$R_\text{series} = R_1 + R_2 + \cdots \qquad \dfrac{1}{R_\text{parallel}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots$Rseries​=R1​+R2​+⋯Rparallel​1​=R1​1​+R2​1​+⋯

$V_\text{out} = V_\text{in} \times \dfrac{R_2}{R_1 + R_2}$Vout​=Vin​×R1​+R2​R2​​

The two constants worth committing to memory are the elementary charge $e = 1.60 \times 10^{-19}\ \text{C}$e=1.60×10−19 C and the free-electron number density of copper, $n \approx 8.5 \times 10^{28}\ \text{m}^{-3}$n≈8.5×1028 m−3, both of which appear in drift-velocity items. The kilowatt-hour, $1\ \text{kWh} = 3.6 \times 10^{6}\ \text{J}$1 kWh=3.6×106 J, is the practical energy unit.

Extended Worked Examples

Worked example 1 — drift velocity

A copper wire of cross-sectional area $1.5 \times 10^{-6}\ \text{m}^2$1.5×10−6 m2 carries a current of $3.0\ \text{A}$3.0 A. Taking $n = 8.5 \times 10^{28}\ \text{m}^{-3}$n=8.5×1028 m−3 and $q = 1.60 \times 10^{-19}\ \text{C}$q=1.60×10−19 C, find the mean drift velocity of the electrons.

Rearranging $I = nAvq$I=nAvq for $v$v:

$v = \dfrac{I}{nAq} = \dfrac{3.0}{8.5 \times 10^{28} \times 1.5 \times 10^{-6} \times 1.60 \times 10^{-19}} \approx 1.5 \times 10^{-4}\ \text{m s}^{-1}$v=nAqI​=8.5×1028×1.5×10−6×1.60×10−193.0​≈1.5×10−4 m s−1

That is about a seventh of a millimetre per second — astonishingly slow. The examinable follow-up is why the light comes on instantly: the electric field that sets the electrons drifting propagates through the wire at close to the speed of light, so every electron starts moving almost simultaneously even though each one crawls.

Worked example 2 — internal resistance from two load conditions

A battery delivers a terminal pd of $11.6\ \text{V}$11.6 V when supplying $2.0\ \text{A}$2.0 A, and $11.2\ \text{V}$11.2 V when supplying $4.0\ \text{A}$4.0 A. Find the EMF and internal resistance.

Using $V = \varepsilon - Ir$V=ε−Ir for both conditions:

$11.6 = \varepsilon - 2.0r \qquad 11.2 = \varepsilon - 4.0r$11.6=ε−2.0r11.2=ε−4.0r

Subtracting the second equation from the first eliminates $\varepsilon$ε:

$0.4 = 2.0r \implies r = 0.20\ \Omega$0.4=2.0r⟹r=0.20 Ω

Substituting back: $\varepsilon = 11.6 + 2.0 \times 0.20 = 12.0\ \text{V}$ε=11.6+2.0×0.20=12.0 V. This is exactly the logic of the PAG measurement, where a graph of terminal pd $V$V against current $I$I gives a straight line: the $y$y-intercept is $\varepsilon$ε and the (negative) gradient is $-r$−r.

Worked example 3 — a potential divider with a thermistor

A $12\ \text{V}$12 V supply feeds a potential divider: a fixed $2.0\ \text{k}\Omega$2.0 kΩ resistor in series with an NTC thermistor. At room temperature the thermistor has resistance $3.0\ \text{k}\Omega$3.0 kΩ; when warmed, its resistance falls to $1.0\ \text{k}\Omega$1.0 kΩ. Find the output voltage across the fixed resistor in each case, and state how the output responds to temperature.

Taking $V_\text{out}$Vout​ across the fixed $2.0\ \text{k}\Omega$2.0 kΩ resistor, $V_\text{out} = V_\text{in} \times R_\text{fixed}/(R_\text{fixed} + R_\text{therm})$Vout​=Vin​×Rfixed​/(Rfixed​+Rtherm​).

At room temperature:

$V_\text{out} = 12 \times \dfrac{2.0}{2.0 + 3.0} = 12 \times 0.40 = 4.8\ \text{V}$Vout​=12×2.0+3.02.0​=12×0.40=4.8 V

When warmed:

$V_\text{out} = 12 \times \dfrac{2.0}{2.0 + 1.0} = 12 \times 0.667 = 8.0\ \text{V}$Vout​=12×2.0+1.02.0​=12×0.667=8.0 V

So as temperature rises, the thermistor's resistance falls, it takes a smaller share of the supply, and the output across the fixed resistor rises. This is the classic temperature-sensor interface: a rising output voltage can trigger a downstream comparator or drive an analogue-to-digital converter in a thermostat.

Worked example 4 — a two-loop Kirchhoff problem

Two cells share a circuit: cell A has EMF $6.0\ \text{V}$6.0 V and negligible internal resistance; cell B has EMF $4.0\ \text{V}$4.0 V and negligible internal resistance. They are connected so both drive current through a common $10\ \Omega$10 Ω resistor, with a $20\ \Omega$20 Ω resistor in cell A's branch and a $30\ \Omega$30 Ω resistor in cell B's branch. Outline the method to find the current in the common resistor.

Label the branch currents $I_1$I1​ (through cell A's branch), $I_2$I2​ (through cell B's branch), and by Kirchhoff's first law the current in the common resistor is $I_1 + I_2$I1​+I2​. Apply Kirchhoff's second law to each loop, declaring a traversal direction and being consistent with signs:

$\text{Loop A:} \quad 6.0 = 20 I_1 + 10(I_1 + I_2)$Loop A:6.0=20I1​+10(I1​+I2​)

$\text{Loop B:} \quad 4.0 = 30 I_2 + 10(I_1 + I_2)$Loop B:4.0=30I2​+10(I1​+I2​)

These are two simultaneous equations in $I_1$I1​ and $I_2$I2​; solving them gives the branch currents, and their sum is the current in the common resistor. The examiner reward is entirely in the setup: currents labelled with chosen directions on the diagram, loops traversed in a declared direction, and EMFs and pd drops entered with consistent signs. A negative answer for a current simply means the true direction is opposite to your guess — which is a legitimate, mark-earning outcome, not an error.

Exam Technique: Turning Knowledge into Marks

On every V = IR step, match the V to the I to the R. The most common circuit error at A-Level is applying Ohm's law with mismatched quantities — dividing a total voltage by a single branch current, for instance. Before you write $V = IR$V=IR, name explicitly which component's V, I and R you are relating. On a multi-loop problem, this discipline is the difference between a clean solution and an inconsistent system.

Declare your sign convention once, at the start, and never change it. For Kirchhoff's second law, pick a traversal direction for each loop and stick with it: an EMF is a rise if you pass through the cell from − to +, and a pd is a drop if you traverse a resistor in the direction of the current you assigned. Consistency, not cleverness, earns the AO2 marks.

For power, pick the formula that uses a quantity you already know. Use $P = I^2 R$P=I2R when the current through the component is known, and $P = V^2/R$P=V2/R when the pd across that specific component is known. The classic trap is computing $P = V^2/R$P=V2/R using the source EMF rather than the pd across the resistor in question — always use the local pd.

Round only at the end. Carry full precision through every intermediate step and round the final answer to a sensible number of significant figures (usually matching the data, typically 2 or 3 s.f.). Premature rounding is a needless accuracy-mark loss.

Mark-scheme literacy

On a typical multi-loop Paper 1 item worth around 12 marks, the AO split is roughly: AO1 (state the two Kirchhoff laws and the combination rules) 3 marks; AO2 (label currents, set up and solve the simultaneous equations, compute the requested pd and power) 6 marks; AO3 (check physical reasonableness — current directions, and an energy balance in which total power delivered by the EMFs equals total power dissipated in all resistances including internal) 3 marks. Candidates routinely bank the AO1 and AO2 marks and forget the AO3 energy-balance check that would confirm the answer and secure the final marks.

Common Mistakes and How to Avoid Them

Mistake 1 — mismatched V and I in Ohm's law. Dividing the total voltage across a series chain by the current through one resistor gives a fictitious "resistance" that means nothing. Always relate a component's own V, I and R.

Mistake 2 — treating EMF as the terminal pd. The terminal pd is always less than the EMF by the "lost volts" $Ir$Ir dissipated inside the cell. Only when no current flows ($I = 0$I=0) does the terminal pd equal the EMF.

Mistake 3 — adding resistances directly in parallel. In parallel it is the reciprocals that add: $1/R_\text{total} = 1/R_1 + 1/R_2 + \cdots$1/Rtotal​=1/R1​+1/R2​+⋯. Writing $R_\text{total} = R_1 + R_2$Rtotal​=R1​+R2​ for a parallel pair is a guaranteed lost mark, and the true parallel resistance is always smaller than the smallest individual resistor.

Mistake 4 — inconsistent signs in Kirchhoff's second law. One EMF or pd entered with the wrong sign produces a self-contradictory simultaneous system. Fix a traversal direction per loop and apply it rigidly.

Mistake 5 — wrong area units in resistivity. In $R = \rho L / A$R=ρL/A, the area must be in $\text{m}^2$m2. A cross-section quoted in $\text{mm}^2$mm2 is out by $10^{-6}$10−6, throwing the resistance out by a factor of a million. Convert $\text{mm}^2 \to \text{m}^2$mm2→m2 by multiplying by $10^{-6}$10−6.

Mistake 6 — using the EMF in $P = V^2/R$P=V2/R. The pd in the power formula must be the pd across the specific component whose power you want, not the source EMF. Find the local pd first, then compute the power.

Mini-FAQ

Why is EMF measured in volts if it is a "force"? The name is historical and misleading — EMF is an energy per unit charge ($\text{J C}^{-1} = \text{V}$J C−1=V), not a force at all. It is the energy a source gives to each coulomb of charge it drives round the circuit. Treat it as a voltage in every calculation.

Why does a filament lamp's resistance rise with temperature but a thermistor's fall? In a metal filament, heating makes the lattice ions vibrate more, so electrons collide more often and resistance rises. In an NTC thermistor (a semiconductor), heating frees more charge carriers, and that effect dominates, so resistance falls. This contrast is a favourite "explain" question.

When is Ohm's law actually valid? Only for ohmic components — those whose resistance is constant over the range of pd used, giving a straight-line I-V graph through the origin (a metal wire at constant temperature). A filament lamp, diode and thermistor are all non-ohmic: their I-V graphs curve. The definition $R = V/I$R=V/I always holds; Ohm's law ($V \propto I$V∝I) does not.

What load gives maximum power transfer from a cell? The load resistance equal to the internal resistance ($R = r$R=r). At that point half the power is delivered to the load and half is wasted inside the cell, so the efficiency is only 50% — a subtle but heavily examined point. Maximum power transfer and maximum efficiency are not the same condition.

Why can I "guess" the current direction in a Kirchhoff problem? Because the maths self-corrects. If you assign a direction and solve, a positive answer confirms your guess and a negative answer tells you the true current flows the other way. Either result is fully correct; you do not need to predict directions in advance.

Authorship and Sign-off

This guide was authored independently by John Haigh, paraphrasing OCR H556 Modules 4.1, 4.2 and 4.3 as descriptive use. I confirm I did not paste from exam-board specification PDFs, mark schemes, examiner reports, or past papers. The worked examples and circuit-analysis scenarios are original.

Start at the Electricity and Circuits course and work through every lesson in sequence. Once Kirchhoff's laws, the resistance combination rules, the internal-resistance correction and the potential-divider relation are automatic, every later H556 module that deploys circuit-style analysis becomes a recognition task rather than a fresh challenge. Module 4 supplies a substantial share of Paper 1 marks and the prerequisite techniques for Capacitors and Fields and the photoelectric circuitry of Quantum Physics, so the investment in fluency here pays back across the whole electromagnetic and modern-physics half of the specification.

Related Reading

• OCR A-Level Physics: Capacitors and Fields — Complete Revision Guide (H556)
• OCR A-Level Physics: Quantum Physics — Complete Revision Guide (H556)
• OCR A-Level Physics: Foundations of Physics — Complete Revision Guide (H556)
• OCR A-Level Physics: Astrophysics and Cosmology — Complete Revision Guide (H556)
• Electricity and Circuits course
• Capacitors and Fields course
• Foundations of Physics course