IB DP Physics: Electric current, resistance and circuits (DP Physics)

This guide covers sub-topic B.5, Current and circuits, from the IB Physics guide (first assessment 2025). The content is the same for SL and HL: the guide adds no extra HL material to this sub-topic. It teaches each understanding from scratch, with worked calculations. For quick recall use the revision notes, then test yourself with the practice questions. Find your gaps first with the free 10-minute diagnostics.

Related pages: the course hub, the printable checklist, work, energy, power and efficiency and the IB DP Physics syllabus guide.

What B.5 covers

Part	What you must be able to do	Tier
B.5	Describe a cell as a source of emf; chemical and solar cells as energy sources	SL and HL
B.5	Read and draw circuit diagrams	SL and HL
B.5	Use I = Δq/Δt and V = W/q	SL and HL
B.5	Explain conductors and insulators using charge-carrier mobility	SL and HL
B.5	Explain the origin of resistance; use R = V/I and ρ = RA/L	SL and HL
B.5	State Ohm’s law; describe ohmic and non-ohmic behaviour and the heating effect	SL and HL
B.5	Use P = IV = I²R = V²/R	SL and HL
B.5	Combine resistors in series and parallel	SL and HL
B.5	Use ε = I(R + r) for a cell with internal resistance	SL and HL
B.5	Describe thermistors, LDRs and potentiometers	SL and HL
B.5	Compare advantages and disadvantages of electrical energy sources	SL and HL

The guide says alternating current circuits are not required, that ammeters and voltmeters are ideal unless the question says otherwise, and that a metal conductor at constant temperature counts as ohmic. It refers you to the Physics data booklet for the circuit symbols you need.

Cells, emf and circuit diagrams

A cell is a device that transfers energy to charge. Its emf ε is the energy transferred to each coulomb of charge as it passes through the cell. The unit is the volt. In a chemical cell, a chemical reaction supplies this energy until the reactants run low. In a solar cell, the energy comes from absorbed light.

A circuit diagram uses standard symbols joined by straight lines to show how components are connected, not where they sit. An ammeter goes in series with the component it measures. A voltmeter goes in parallel across it. Learn the symbols for a cell, battery, switch, lamp, resistor, variable resistor, thermistor, LDR, ammeter and voltmeter.

Current and potential difference

Direct current is a flow of charge carriers in one direction. In metals the carriers are electrons, but conventional current is drawn in the direction a positive charge would move.

• Current: I = Δq/Δt, with I in amperes, q in coulombs and t in seconds.
• Potential difference: V = W/q. One volt is one joule of energy transferred per coulomb moved from one point to another along the route the current takes.

Worked example 1. A lamp carries 0.42 A for 15 minutes across a 4.5 V supply.

• Time = 15 × 60 = 900 s.
• Charge: q = IΔt = 0.42 × 900 = 378 C.
• Electrons passing (e = 1.60 × 10⁻¹⁹ C): 378 ÷ 1.60 × 10⁻¹⁹ = 2.4 × 10²¹.
• Energy transferred: W = Vq = 4.5 × 378 = 1.7 × 10³ J.

Conductors, insulators and the origin of resistance

A conductor contains many charge carriers that can move freely. A metal has a lattice of positive ions and a large number of mobile electrons. An insulator has almost no mobile carriers, so the same p.d. produces a negligible current. Mobility is how readily carriers move through the material when a p.d. is applied.

Resistance comes from collisions. Carriers accelerate in the field, then collide with the vibrating ions and transfer energy to them. This energy appears as thermal energy in the lattice. Anything that makes collisions more frequent raises the resistance. In a metal, a higher temperature means larger lattice vibrations and more collisions, so resistance rises.

Resistance, resistivity and Ohm’s law

Resistance is defined by R = V/I, in ohms (V A⁻¹). It is a ratio at one point. It is not the gradient of a graph unless the graph is a straight line through the origin.

For a uniform wire, resistance depends on the material and the shape:

R = ρL/A, which rearranges to ρ = RA/L

Resistivity ρ belongs to the material (at a given temperature). Its unit is the ohm metre (Ω m). Resistance rises with length and falls with cross-sectional area.

Worked example 2. A nichrome wire has length 2.5 m and diameter 0.40 mm. Its resistivity is 1.1 × 10⁻⁶ Ω m (given).

• Radius = 0.20 × 10⁻³ m, so A = πr² = π × (0.20 × 10⁻³)² = 1.26 × 10⁻⁷ m².
• R = ρL/A = (1.1 × 10⁻⁶ × 2.5) ÷ 1.26 × 10⁻⁷ = 22 Ω.
• If the diameter doubles, A is four times larger, so R falls to a quarter: 5.5 Ω.

Ohm’s law: for a conductor at constant temperature, the current is directly proportional to the p.d. across it. A device that obeys this is ohmic, and its V against I graph is a straight line through the origin.

Ohmic and non-ohmic behaviour, and heating

A metal wire at constant temperature is ohmic. A filament lamp is not: as current rises, the filament heats up, the lattice vibrates more, and R increases. The I–V graph bends towards the V axis. A thermistor and an LDR are also non-ohmic.

Worked example 3. A filament lamp has 3.0 V across it at 0.25 A, and 9.0 V at 0.50 A.

• R at 3.0 V: 3.0 ÷ 0.25 = 12 Ω.
• R at 9.0 V: 9.0 ÷ 0.50 = 18 Ω.
• Tripling the p.d. did not triple the current, so the lamp is non-ohmic. The rise in R matches the rise in filament temperature.

Electrical power

The power dissipated in a component is P = IV. Using V = IR gives two more forms:

P = IV = I²R = V²/R

Choose the form that uses the quantities you know. Use I²R when the same current flows through resistors in series. Use V²/R when the same p.d. is across resistors in parallel.

Worked example 4. A heater element is rated 36 W at 12 V.

• I = P/V = 36 ÷ 12 = 3.0 A.
• R = V²/P = 12² ÷ 36 = 4.0 Ω.
• Energy in 5.0 minutes: W = Pt = 36 × 300 = 1.1 × 10⁴ J.

Resistors in series and parallel

	Series	Parallel
Current	I = I₁ = I₂	I = I₁ + I₂
p.d.	V = V₁ + V₂	V = V₁ = V₂
Resistance	Rs = R₁ + R₂	1/Rp = 1/R₁ + 1/R₂

Adding a resistor in series always raises the total. Adding one in parallel always lowers it, so Rp is smaller than the smallest branch.

Worked example 5. An ideal 9.0 V cell is connected to a 4.8 Ω resistor in series with a parallel pair of 12 Ω and 18 Ω.

• 1/Rp = 1/12 + 1/18 = 5/36, so Rp = 7.2 Ω.
• Total R = 7.2 + 4.8 = 12.0 Ω, so I = 9.0 ÷ 12.0 = 0.75 A.
• p.d. across the pair = 0.75 × 7.2 = 5.4 V. (Check: across the 4.8 Ω resistor, 0.75 × 4.8 = 3.6 V, and 5.4 + 3.6 = 9.0 V.)
• Branch currents: 5.4 ÷ 12 = 0.45 A and 5.4 ÷ 18 = 0.30 A, which sum to 0.75 A.

Emf and internal resistance

A real cell has resistance r inside it. Charge must pass through this as well as the external resistance R, so

ε = I(R + r)

The terminal p.d. is V = IR = ε − Ir. The term Ir is the p.d. wasted inside the cell, sometimes called the lost volts. It grows with current. A graph of terminal p.d. (y) against current (x) is a straight line with intercept ε and gradient −r. The short-circuit current is ε/r.

Worked example 6. A cell drives a current of 1.0 A through a 5.0 Ω resistor, and 2.0 A through a 2.0 Ω resistor.

• First case: ε = 1.0(5.0 + r). Second case: ε = 2.0(2.0 + r).
• Equate: 5.0 + r = 4.0 + 2.0r, so r = 1.0 Ω.
• ε = 1.0 × 6.0 = 6.0 V.
• Terminal p.d. in the first case = 1.0 × 5.0 = 5.0 V, and 1.0 V is lost inside the cell.

Variable resistors and ideal meters

• Thermistor: its resistance depends on temperature. For the common type, resistance falls as temperature rises, because heating frees more charge carriers.
• LDR (light-dependent resistor): its resistance falls as light intensity rises.
• Potentiometer: a resistor with a sliding contact. Connected across a supply, it divides the p.d. so the output can be set anywhere from zero to the full supply value.

A thermistor or LDR in series with a fixed resistor forms a potential divider, and the p.d. divides in proportion to the resistances.

Worked example 7. A 6.0 V supply is across a 3.0 kΩ fixed resistor in series with a thermistor.

• At 25 °C the thermistor is 1.5 kΩ. Its share is 6.0 × 1.5 ÷ (3.0 + 1.5) = 2.0 V.
• When hot it is 0.50 kΩ: 6.0 × 0.50 ÷ 3.5 = 0.86 V.
• The p.d. across the thermistor falls as it warms, and the p.d. across the fixed resistor rises.

An ideal ammeter has zero resistance. An ideal voltmeter has infinite resistance, so it draws no current. If a question gives a non-ideal meter, treat its resistance as constant and include it in the circuit like any resistor.

Sources of electrical energy

• Chemical cells: portable and give a steady p.d., but the energy store is small, the p.d. falls as they run down, and the materials must be disposed of or recycled.
• Solar cells: no fuel and no emissions in use, but the output depends on light intensity and weather, they need a large area for high power, and only part of the incident light power becomes electrical.
• Other sources you may be asked to compare, such as fossil fuels, nuclear, wind, hydroelectric: give one advantage and one disadvantage in terms of reliability, cost, emissions or land use.

Common errors

• Putting the voltmeter in series, or the ammeter in parallel.
• Using R = V/I as a gradient for a curved I–V graph.
• Doubling the radius instead of the diameter, or forgetting to square it, in ρ = RA/L.
• Using millimetres in A without converting to metres: 1 mm² is 10⁻⁶ m².
• Adding reciprocals in parallel but forgetting to invert at the end.
• Treating terminal p.d. as equal to emf when current flows.
• Saying resistance rises because “electrons slow down” without mentioning lattice collisions.

Official syllabus

Source: Physics guide, first assessment 2025, International Baccalaureate Organization (Diploma Programme), sub-topic B.5 Current and circuits.