IB Physics Electricity & Circuits Explained

Electricity and circuits in IB Physics centre on a small set of connected ideas: charge flow, potential difference, resistance, power, resistor combinations, and real cells. To earn marks consistently, you must do more than recall equations. You need to identify what stays constant in each circuit arrangement, interpret graphs correctly, and show a logical calculation method.

In the current course, first assessed in 2025, this material appears in B.5 Current and circuits and contains no separate additional higher level content. However, it can be combined with unfamiliar data, graph analysis, uncertainty, and multi-step reasoning in both SL and HL examinations. This guide explains the physics, the question styles examiners use, and the methods that convert understanding into marks.

Where electricity and circuits appear in IB Physics exams

The official IB Physics subject brief explains that Paper 1 contains multiple-choice and data-based questions, while Paper 2 contains short-answer and extended-response questions. Electricity can therefore appear as a rapid calculation, a circuit diagram, an investigation, an unfamiliar current-voltage graph, or one stage of a longer problem.

Common instructions include:

• Calculate current, resistance, power, terminal potential difference, or energy transferred.
• Determine an unknown quantity from a graph or circuit arrangement.
• Explain non-ohmic behaviour or why terminal voltage changes.
• Sketch a current-voltage characteristic or show the effect of changing resistance.
• Deduce how changing a wire's dimensions affects resistance or power.

The equations are supplied in the Physics data booklet, but the booklet does not decide which equation applies. Equation selection and circuit reasoning remain essential exam skills.

Current, charge, potential difference, and emf

Current is the rate of charge flow

Electric current is defined by

$I=\frac{\Delta q}{\Delta t}$

where $I$ is current in amperes, $\Delta q$ is charge in coulombs, and $\Delta t$ is time in seconds. A current of $2.0\ \text{A}$ means that $2.0\ \text{C}$ of charge passes a point each second.

In a metal, electrons move toward the positive terminal, but conventional current is defined in the opposite direction, from positive to negative. Do not reverse current arrows merely because the mobile charge carriers are electrons.

Potential difference measures energy transfer

Potential difference is the work done, or energy transferred, per unit charge:

$V=\frac{W}{q}$

A potential difference of $6.0\ \text{V}$ means that $6.0\ \text{J}$ is transferred per coulomb. Across a resistor, electrical energy is commonly transferred into thermal energy.

Electromotive force, or emf, is also measured in volts, but describes the energy supplied per unit charge by a source. Despite its name, emf is not a force. This distinction matters when a question compares a cell's emf with its terminal potential difference.

Resistance, resistivity, and Ohm's law

Resistance is defined as

$R=\frac{V}{I}$

It measures how strongly a component opposes current. Microscopically, resistance in a metal arises as moving charge carriers interact with the lattice, transferring energy to it.

For a uniform wire,

$R=\rho\frac{L}{A}$

where $\rho$ is the material's resistivity, $L$ is length, and $A$ is cross-sectional area. Resistance depends on both material and dimensions, whereas resistivity is a property of the material under specified physical conditions, including temperature.

Change to a uniform wire	Effect on resistance
Double its length	Resistance doubles
Double its cross-sectional area	Resistance halves
Double its diameter	Area becomes four times larger, so resistance becomes one quarter
Replace it with a higher-resistivity material	Resistance increases

Diameter questions are a frequent trap because $A=\pi d^2/4$. If the diameter changes by a factor of two, area does not change by a factor of two.

Ohmic and non-ohmic behaviour

Ohm's law states that current is directly proportional to potential difference for an ohmic conductor when relevant physical conditions, particularly temperature, remain constant. Its resistance is therefore constant and its $I$-$V$ graph is a straight line through the origin.

A filament lamp is non-ohmic because increasing current raises the filament's temperature. The hotter lattice causes more frequent interactions with electrons, so resistance increases and the graph curves. Examiners often expect this causal chain, not merely the statement that the graph is non-linear.

Be careful with graph orientation. On an $I$ against $V$ graph, gradient is $I/V=1/R$; on a $V$ against $I$ graph, gradient is .

Series and parallel circuits

Circuit analysis becomes manageable once you identify which quantity is shared.

Arrangement	Current	Potential difference	Equivalent resistance
Series	Same through every component	Divided across components	$R_s=R_1+R_2+\cdots$

For two parallel resistors, the shortcut $R_p=R_1R_2/(R_1+R_2)$ is useful. The equivalent resistance must be smaller than the smallest branch resistance, providing an immediate check on your result.

These rules reflect conservation principles. At a junction, total current entering equals total current leaving because charge is conserved. Around a complete loop, the algebraic sum of potential changes is zero because energy is conserved. These are commonly called Kirchhoff's junction and loop rules.

A reliable circuit-solving method

1. Redraw the circuit clearly and label known values.
2. Identify definite series or parallel groups.
3. Calculate the equivalent external resistance.
4. Find total current from the source.
5. Work back outward to obtain branch currents or component voltages.
6. Check conservation of current at junctions and voltage around loops.

For example, suppose $6.0\ \Omega$ and $3.0\ \Omega$ resistors are connected in parallel across $12\ \text{V}$. Their equivalent resistance is $2.0\ \Omega$, so the total current is $6.0\ \text{A}$. Because each branch has across it, the branch currents are and , which add to the total.

Electrical power and energy

Electrical power is the rate of energy transfer:

$P=IV=I^2R=\frac{V^2}{R}$

Choose the form containing the quantities known or held constant. This last condition matters because statements such as "greater resistance produces greater power" are incomplete.

• At constant current, $P=I^2R$, so increasing $R$ increases power.
• At constant potential difference, $P=V^2/R$, so increasing decreases power.

Electrical energy transferred over time is

$E=Pt=VIt$

A strong response includes a numerical answer, unit, and sensible significant figures. If a question asks for energy rather than power, stopping after calculating watts does not answer it.

Emf, internal resistance, and terminal voltage

A real cell is modelled as an ideal emf source  in series with internal resistance $r$. When it supplies current to an external resistance $R$,

$\varepsilon=I(R+r)$

and

$V_{\text{terminal}}=\varepsilon-Ir=IR$

The quantity $Ir$ is sometimes called the lost volts, representing energy transferred per unit charge inside the cell. When no current flows, $Ir=0$, so the terminal potential difference equals the emf.

Example: a cell has emf $6.0\ \text{V}$ and internal resistance $0.50\ \Omega$, connected to a $2.5\ \Omega$ load. The current is

$I=\frac{6.0}{2.5+0.50}=2.0\ \text{A}$

so the terminal voltage is $V=IR=5.0\ \text{V}$. The remaining $1.0\ \text{V}$ is the potential difference across the internal resistance.

A graph of terminal voltage against current follows $V=\varepsilon-Ir$. Therefore, the vertical intercept gives emf and the magnitude of the gradient gives internal resistance. This is a common way for data-based questions to connect circuit theory with graph analysis.

Meters, circuit diagrams, and practical questions

An ammeter measures current and is connected in series. An ideal ammeter has zero resistance so it does not significantly reduce the current.

A voltmeter measures potential difference and is connected in parallel across a component. An ideal voltmeter has infinite resistance so it draws no current. Connecting an ammeter directly across a source creates a very low-resistance path and can produce a dangerously large current.

In practical questions, examiners may ask how to investigate the $I$-$V$ characteristic of a component. A suitable method varies the potential difference using a variable resistor or adjustable supply, measures current and voltage for several settings, and controls relevant conditions. If testing Ohm's law for a metal wire, keeping temperature approximately constant is particularly important.

Common mistakes that lose marks

• Treating emf and terminal potential difference as automatically equal.
• Adding parallel resistances directly instead of adding reciprocals.
• Assuming current is divided in a series circuit.
• Assuming potential difference is divided between parallel branches.
• Using the gradient of an $I$-$V$ graph as resistance rather than conductance.
• Applying $V=IR$ as evidence that every component obeys Ohm's law.
• Ignoring the square when diameter changes in a resistivity problem.
• Substituting values before simplifying the circuit structure.
• Giving an unexplained answer when the command term is explain.

A useful diagnostic question is: What is fixed here: current, voltage, resistance, material, or geometry? That usually determines the correct relationship.

How to revise circuits for exam marks

Begin with the B.5 Current and circuits notes, then practise one skill at a time in the B.5 circuits Questionbank. Separate errors into conceptual mistakes, circuit-reading mistakes, algebra, and units rather than recording only that an answer was wrong.

The fastest way to see how theory becomes marks is to watch the method applied line by line. RevisionDojo's B.5 electricity and circuits video solutions and current and voltage worked videos show how circuit information is translated into equations. Follow each video by attempting a similar question without assistance.

Use IB Physics Flashcards for definitions and conditions, not as a substitute for calculations. Near the exam, complete Physics Predicted Papers under timed conditions and use Jojo AI to analyse repeated weaknesses in your written method.

Conclusion

IB Physics electricity and circuits become much more predictable when every problem is reduced to charge flow, energy per charge, resistance, conservation, and power. Know what remains constant in series and parallel arrangements, distinguish emf from terminal voltage, and interpret graph gradients according to the axes shown.

RevisionDojo can support this process with B.5 Study Notes, targeted Questionbank practice, and worked video solutions. After learning each idea, the most useful next step is to attempt an exam-style question and compare your reasoning with the full solution method.

Sources and referenced URLs

• Official IB Physics subject brief, first assessment 2025
• Official IB Physics curriculum update
• IB Physics guide, first assessment 2025
• MIT OpenCourseWare DC circuits and Kirchhoff's rules
• RevisionDojo B.5 Current and circuits notes
• RevisionDojo B.5 Current and circuits Questionbank
• RevisionDojo B.5 electricity and circuits videos
• RevisionDojo B.5.2 current and voltage videos
• RevisionDojo IB Physics Flashcards
• RevisionDojo Physics Predicted Papers