What does Current and Circuits cover in IB Physics?

This topic introduces direct current (DC) circuits, covering sources of electromotive force (emf) and the flow of charge. Current is I = Δ Q / Δ t. Electric potential difference is V = W/q.

Is Current and Circuits SL or HL?

Both. SL and HL students study Current and Circuits to the same depth.

How does FourtyFive help me practise Current and Circuits?

FourtyFive has 12 Current and Circuits questions. Every answer you write is marked mark by mark, IB-style, and you see where each mark was won or lost. Every part has a hint, the AI tutor helps you through the step you are stuck on, and your Study Profile picks what to practise next.

Is FourtyFive free for Current and Circuits practice?

Yes. A free account gives you 50 marked answers a month, and you do not need a card to sign up.

Can I handwrite Current and Circuits answers on an iPad?

Yes. In the FourtyFive iPad app you write your working by hand with Apple Pencil, the way you would on paper, and it is marked the same way.

Topic B.5 · SL and HL

Current and Circuits: notes and practice questions

Q: How do I revise Current and Circuits for IB Physics?

Start from the core idea: this topic introduces direct current (DC) circuits, covering sources of electromotive force (emf) and the flow of charge. In the exam: both papers. Paper 2 questions are typically a V-I graph with a non-ohmic component in series with an ohmic one. Then practise exam-style questions, easiest first, writing out every step of your working before you check it.

9 min read Jump to 12 practice questions

Summary

This topic introduces direct current (DC) circuits, covering sources of electromotive force (emf) and the flow of charge.
Current is $I = \Delta Q / \Delta t$ .
Electric potential difference is $V = W/q$ .
Electrical resistance is $R = V/I$ .
Resistivity is $\rho = RA/L$ .
Electrical power dissipated by a resistor is $P = IV = I^2R = V^2/R$ .
Resistors in series: $R_{total} = R_1 + R_2 + \dots$ .
Resistors in parallel: $1/R_{total} = 1/R_1 + 1/R_2 + \dots$ .
Cells have emf $\varepsilon$ and internal resistance $r$ , with $\varepsilon = I(R+r)$ .
Ohm's law describes ohmic conductors; non-ohmic behaviour and variable resistors are also studied.

How it is examined

Both papers. Paper 2 questions are typically a V-I graph with a non-ohmic component in series with an ohmic one. May 2025 SL Paper 2 TZ1 question 3 did exactly that across four short parts, 1 + 1 + 1 + 2 marks: calculate a resistance from the graph, outline how a non-ohmic resistance changes with current, state an ammeter reading in a stated unit, determine the emf. The mark scheme gave two full alternative routes for the emf part, which is normal in circuits. ac circuits are explicitly excluded: never generate one.

Given in the booklet

$I = \Delta q/\Delta t$ , $V = W/q$ , $R = V/I$ , $\rho = RA/L$ , the three power forms, the series and parallel combination rules, $\varepsilon = I(R + r)$ . The booklet also carries the full set of electrical circuit symbols, which the guidance points at directly, so a circuit diagram in a question may use any of them without a key.

Key ideas

that cells provide a source of emf
chemical cells and solar cells as the energy source in circuits
that circuit diagrams represent the arrangement of components in a circuit
direct current (dc) I as a flow of charge carriers, as given by $I = \dfrac{\Delta q}{\Delta t}$

Not assessed

Alternating current (ac) circuits are not required.

Guiding questions

How do charged particles flow through materials?
How are the electrical properties of materials quantified?
What are the consequences of resistance in conductors?

Linking questions

In what ways can an electrical circuit be described as a system like the Earth's atmosphere or a heat engine?
How are the fields in other areas of physics similar to and different from each other?
How can the heating of an electrical resistor be explained using other areas of physics?
What are the advantages of cells as a source of electrical energy?
How does a particle model allow electrical resistance to be explained? (NOS)
What are the parallels in the models for thermal and electrical conductivity? (NOS)

Practice questions

12 questions · 2 easy · 9 medium · 1 hard

Showing 12 of 12

Question 1

EasyPaper 1A · calculator1 mark

Two cylindrical resistors, X and Y, are connected in series to a cell. Resistor X has twice the length and half the diameter of resistor Y. Both resistors are made of the same material.

The current in X is $I_\text{X}$ and the current in Y is $I_\text{Y}$ . What is the ratio $\frac{I_\text{X}}{I_\text{Y}}$ ?

A. $\frac{1}{8}$

B. $1$

C. $2$

D. $8$

Question 2

MediumPaper 2 · calculator11 marks

(a)

A portable power supply, designed for drone operation, consists of a battery with an internal resistance. It is initially connected to two identical heating elements, each with a resistance of $4.0\ \Omega$ , arranged in parallel. The total current drawn from the power supply in this configuration is $3.0\ \text{A}$ .

For a different operational mode, the two heating elements are reconnected in series to the same power supply. In this series configuration, the total current drawn from the power supply is $1.0\ \text{A}$ .

(a) Calculate the internal resistance of the power supply.

[3]

(b)

(b) Determine the electromotive force (emf) of the power supply.

[3]

(c)(i)

i. when connected in parallel.

[3]

(c)(ii)

ii. when connected in series.

[2]

Question 3

HardPaper 2 · calculator18 marks

(a)

An electric ski lift is powered by a motor at the base station. The motor is connected to a 750 V DC power supply by a cable with a total resistance of 0.15 Ω. When operating at full capacity, the motor draws a constant current of 400 A.

(a) Determine the potential difference across the terminals of the motor.

[2]

(b)

(b) The motor has an efficiency of 92%. Calculate the useful mechanical power output of the motor.

[2]

(c)

The ski lift carries skiers up a slope of length 1800 m that rises by a vertical height of 500 m. There are 50 chairs on the ascending side. Each empty chair has a mass of 25 kg and carries, on average, 1.5 skiers of average mass 75 kg. A constant resistive force of 12 kN opposes the motion.

[3]

(d)

(d) Estimate the maximum speed, $v$ , of the ski lift.

[2]

(e)

(e) The lift operates continuously. Estimate the maximum number of skiers that can be transported to the top station in one hour.

[3]

(f)

(f) In an emergency stop, a brake is applied to a large solid steel disc, bringing the lift to a halt from its maximum speed. The total mass of the moving system (chairs, skiers, and cable) is 18 000 kg. Assume all the kinetic energy of the system is converted into thermal energy in the brake disc.

Calculate the temperature rise of the disc.

Data for this question:
Brake disc radius = 0.75 m
Brake disc thickness = 0.10 m
Density of steel = 7850 kg m⁻³
Specific heat capacity of steel = 450 J kg⁻¹ K⁻¹

[4]

(g)

(g) The speed of a chair is monitored using a radar device at the base station that emits microwaves of frequency 30 GHz. It measures the waves reflected from a chair as it moves away. The frequency shift, $Δf$ , for a source moving directly away from a stationary observer can be approximated by the formula $Δf/f ≈ v/c$ . In this radar measurement, this formula gives a good approximation for the shift detected.

Calculate the expected frequency shift.

[2]

Question 4

EasyPaper 2 · calculator3 marks

An electrical heater is completely immersed in a container of liquid nitrogen which is at its boiling point. The heater operates with a potential difference of $14 \text{ V}$ and a current of $2.5 \text{ A}$ . The specific latent heat of vaporization of nitrogen is $2.0 \times 10^5 \text{ J}\,\text{kg}^{-1}$ .

Calculate the time taken for $70 \text{ g}$ of the liquid nitrogen to vaporize.

Question 5

MediumPaper 1A · calculator1 mark

Four identical resistors are connected as shown. The current at point X is $I_X$ and the current at point Y is $I_Y$ .

A schematic diagram of an electrical circuit connected to a DC voltage source on the left. The main wire from the positive terminal splits into two distinct parallel branches. The top branch consists of two identical resistors, each labeled R, connected in series; a measurement point X is located on the wire between these two resistors. The bottom branch features a measurement point Y on its initial wire, which then immediately splits into a nested parallel sub-circuit containing two identical resistors, also labeled R, before recombining. The top and bottom branches finally merge back together and return to the negative terminal of the voltage source.

What is the ratio $\frac{I_X}{I_Y}$ ?

A. $\frac{1}{4}$

B. $\frac{1}{2}$

C. $2$

D. $4$

Question 6

MediumPaper 1A · calculator1 mark

A student is designing a heating system for a small model house using three resistive heating elements. Two heating elements, $R_1$ and $R_2$ , are connected in series. This series combination is then connected in parallel with a third heating element, $R_3$ .

Given that $R_1 = 10 \, \Omega$ , $R_2 = 15 \, \Omega$ , and $R_3 = 20 \, \Omega$ , what is the total equivalent resistance of this circuit?

A. $4.62 \, \Omega$

B. $11.1 \, \Omega$

C. $25.0 \, \Omega$

D. $45.0 \, \Omega$

Question 7

MediumPaper 1A · calculator1 mark

A heating element in a laboratory hot plate is made from a wire of length $L$ . When a potential difference of $120\text{ V}$ is applied across the wire, the power dissipated is $360\text{ W}$ . A second heating element is constructed using a wire made from the same material and with the same cross-sectional area. When a potential difference of $240\text{ V}$ is applied across the second wire, the power dissipated is $720\text{ W}$ .

What is the length of the second wire?

A. $\frac{L}{2}$

B. $L$

C. $2L$

D. $4L$

Question 8

MediumPaper 1A · calculator1 mark

A heating coil (Coil A) in an electric kettle dissipates a power of $16 \text{ W}$ when connected to a voltage $V$ .

Another heating coil (Coil B) is made from the same resistive wire material and has the same length as Coil A, but its diameter is half that of Coil A.

Coil B is connected to a voltage of $1.5V$ .

Both coils are assumed to have negligible temperature change effects on resistance.

What power is dissipated in Coil B?

A. $4.0 \text{ W}$

B. $8.0 \text{ W}$

C. $9.0 \text{ W}$

D. $18 \text{ W}$

Question 9

MediumPaper 1A · calculator1 mark

A filament lamp, bulb A, is rated to dissipate $24 \text{ W}$ when connected to a $12 \text{ V}$ supply.

A second lamp, bulb B, has a filament made of the same material and with the same diameter as bulb A, but the filament is half as long.

Bulb B is connected to a $6.0 \text{ V}$ supply.

Both supplies have negligible internal resistance.

What is the power dissipated in bulb B?

A. $6.0 \text{ W}$

B. $12 \text{ W}$

C. $24 \text{ W}$

D. $48 \text{ W}$

Question 10

MediumPaper 2 · calculator7 marks

(a)

A student performs an experiment to determine the resistivity of a metal wire. The resistance $R$ , length $L$ , and diameter $d$ of the wire are measured.

(a) The diameter is measured with a micrometer screw gauge. State one experimental precaution that should be taken to ensure this measurement is accurate.

[1]

(b)

(b) The following data are collected:

Resistance $R = (5.2 \pm 0.1) \, \Omega$

Length $L = (1.50 \pm 0.01) \, \text{m}$

Diameter $d = (0.45 \pm 0.02) \, \text{mm}$

Calculate the resistivity of the wire and its absolute uncertainty.

[3]

(c)

[1]

(d)

(d) The accepted value for the resistivity of nichrome at the experimental temperature is $1.10 \times 10^{-6} \, \Omega \text{ m}$ . Deduce, using your answer from (c), whether the wire is likely to be made of nichrome.

[2]

Question 11

MediumPaper 1A · calculator1 mark

A current $I$ in a wire of length $L$ and diameter $d$ dissipates a power of 400 W. A second wire of the same material has length $2L$ and diameter $2d$ . What is the power dissipated in the second wire when it carries the same current $I$ ?

A. 100 W

B. 200 W

C. 400 W

D. 800 W

Question 12

MediumPaper 2 · calculator10 marks

(a)

A cell of electromotive force (emf) $\varepsilon$ and internal resistance $r$ is connected in series with an ideal ammeter and a resistor of resistance $4.0\text{ }\Omega$ . The ammeter reading is $1.5\text{ A}$ .

A second resistor of resistance $6.0\text{ }\Omega$ is then connected in parallel with the $4.0\text{ }\Omega$ resistor. The ammeter reading increases to $2.0\text{ A}$ .

(a) Determine the internal resistance $r$ of the cell.

[3]

(b)

(b) Calculate the emf $\varepsilon$ of the cell.

[1]

(c)

(c) Determine the change in the power dissipated by the $4.0\text{ }\Omega$ resistor when the $6.0\text{ }\Omega$ resistor is added to the circuit.

[3]

(d)

(d) The $6.0\text{ }\Omega$ resistor is removed and replaced by a variable resistor. Explain how the terminal potential difference of the cell changes as the resistance of the variable resistor is decreased.

[3]

Every Current and Circuits question, marked for you

Every answer is marked mark by mark, IB-style, and the AI tutor helps when you are stuck.

Where marks are lost

Stopping one step short of the conclusion. Two numbers and no sentence is two marks out of three.
Answering a procedure question with a platitude.
Losing precision in Paper 1B. Uniquely to this paper, quoting the right number badly loses marks.

Current and Circuits: notes and practice questions

How it is examined

Guiding questions

Linking questions