Five resistors of equal resistance are connected to a cell as shown.

What is correct about the power dissipated in the resistors?

A.     The power dissipated is greatest in resistor X.

B.     The power dissipated is greatest in resistor Y.

C.     The power dissipated is greatest in resistor Z.

D.     The power dissipated is the same in all resistors.

C

The electromotive force (emf) of a cell is defined as

A.     the power supplied by the cell per unit current from the cell.

B.     the force that the cell provides to drive electrons round a circuit.

C.     the energy supplied by the cell per unit current from the cell.

D.     the potential difference across the terminals of the cell.

A

At both levels the most popular response was D, with A, the correct answer, being the least popular. It must be stressed that candidates are expected to learn rigorous definitions.

A current is established in a coil of wire in the direction shown.

The direction of the magnetic field at point P is

A.     out of the plane of the paper.

B.     into the plane of the paper.

C.     to the left.

D.     to the right.

B

A cell with negligible internal resistance is connected as shown. The ammeter and the voltmeter are both ideal. 

What changes occur in the ammeter reading and in the voltmeter reading when the resistance of the variable resistor is increased?

C

Which diagram best represents the electric field due to a negatively charged conducting sphere?

C

The circuit shows a resistor R connected in series with a battery and a resistor of resistance \({\text{10 }}\Omega \). The emf of the battery is 20 V and it has negligible internal resistance. The current in the circuit is 1.0 A.

Which of the following is the resistance of R?

A.     \({\text{1.0 }}\Omega \)

B.     \({\text{2.0 }}\Omega \)

C.     \({\text{10 }}\Omega \)

D.     \({\text{20 }}\Omega \)

C

Three identical resistors are connected to a battery as shown.

Which of the following is a correct statement?

A.     The current through X is greater than that through Z.

B.     The potential difference across Z is greater than that across Y.

C.     The potential difference across resistor X and Y together is the same as that across Z.

D.     The current through Z is less than the total current through X and Y.

B

The diagram shows two current-carrying wires, P and Q, that both lie in the plane of the paper. The arrows show the conventional current direction in the wires.

The electromagnetic force on Q is in the same plane as that of the wires. What is the direction of the electromagnetic force acting on Q?

A

A positively-charged particle moves parallel to a wire that carries a current upwards.

What is the direction of the magnetic force on the particle?

A.  To the left

B.  To the right

C.  Into the page

D.  Out of the page

A

An electron travelling at speed v perpendicular to a magnetic field of strength B experiences a force F.

What is the force acting on an alpha particle travelling at 2v parallel to a magnetic field of strength 2B?

A.  0

B.  2F

C.  4F

D.  8F

A

An electron is accelerated through a potential difference of 2.5 MV. What is the change in kinetic energy of the electron?

A.  0.4μJ

B.  0.4 nJ

C.  0.4 pJ

D.  0.4 fJ

C

Which of the following diagrams illustrates the electric field pattern of a negatively charged sphere?

A

In the circuits below the cells have the same emf and zero internal resistance. The resistors all have the same resistance.

Which of the following gives the ratio \(\frac{{{\text{power dissipated in X}}}}{{{\text{power dissipated in Y}}}}\)?

A.     \(\frac{1}{4}\)

B.     \(\frac{1}{2}\)

C.     2

D.     4

D

A positively charged particle enters the space between two charged conducting plates, with a constant velocity directed parallel to the plates, as shown.

The top plate is positively charged and the bottom plate is negatively charged. There is a magnetic field in the shaded region PQRS. The particle continues to move in a horizontal straight line between the plates. Which of the following correctly describes the magnetic field direction?

A.     Into plane of paper

B.     Out of plane of paper

C.     Up

D.     Down

A

A beam of electrons moves between the poles of a magnet.

What is the direction in which the electrons will be deflected?

A.     Downwards

B.     Towards the N pole of the magnet

C.     Towards the S pole of the magnet

D.     Upwards

D

A cell has an emf of 4.0 V and an internal resistance of 2.0 Ω. The ideal voltmeter reads 3.2 V.

What is the resistance of R?

A.     0.8 Ω

B.     2.0 Ω

C.     4.0 Ω

D.     8.0 Ω

D

Three resistors are connected as shown. What is the value of the total resistance between X and Y?

A.     1.5 Ω

B.     1.9 Ω

C.     6.0 Ω

D.     8.0 Ω

A

Two resistors X and Y are made of uniform cylinders of the same material. X and Y are connected in series. X and Y are of equal length and the diameter of Y is twice the diameter of X.

The resistance of Y is R.

What is the resistance of this series combination?

A.     \(\frac{{5R}}{4}\)

B.     \(\frac{{3R}}{2}\)

C.     3R

D.     5R

D

A metal wire X with length L and radius r has a resistance R. A wire Y of length 4L made from the same material as X has the same resistance R. What is the radius of Y?

A. 2r

B. 4r

C. \(\frac{r}{2}\)

D. \(\frac{r}{4}\)

A

A cylindrical resistor of length \(l\) is made from a metal of mass \(m\). It has a resistance \(R\).

Two resistors, each of length \(2l\) and mass \(\frac{m}{2}\), are then created from the same volume of the metal.

What is the resistance of the two resistors when connected in parallel?

A.     \(R\)

B.     \(2R\)

C.     \(4R\)

D.     \(8R\)

C

Think proportionality.

There were a few G2 comments suggesting that this question was too complex and took too much time, but this is only the case if candidates reach for equations before considering proportionality.

A simple sketch will show that if the new resistors are placed side by side (ie in parallel) then the new length is twice the previous length (leading to a doubling of the resistance) and half its cross-sectional area (leading to a further doubling of the resistance). So the correct response is C.

Two rectangular blocks, \(X\) and \(Y\), of the same material have different dimensions but the same overall resistance. Which of the following equations is correct?

A.     resistivity of \(X \times {\text{length of }}X = {\text{resistivity}}\) of \(Y \times {\text{length of }}Y\)

B.     \(\frac{{{\text{length of }}X}}{{{\text{cross sectional area of }}X}} = \frac{{{\text{length of }}Y}}{{{\text{cross sectional area of Y}}}}\)

C.     resistivity of \(X \times {\text{cross sectional area of }}X = {\text{resistivity of }}Y \times {\text{cross sectional area of }}Y\)

D.     \(\frac{{{\text{length of }}X}}{{{\text{cross sectional area of }}Y}} = \frac{{{\text{length of }}Y}}{{{\text{cross sectional area of }}X}}\)

B

A cell of \({\text{emf }}\varepsilon \) and internal resistance \(r\) delivers current to a small electric motor.

450 C of charge flows through the motor and 9000 J of energy are converted in the motor. 1800 J are dissipated in the cell. The emf of the cell is

A.     4.0 V.

B.     16 V.

C.     20 V.

D.     24 V.

D

A resistor of resistance \({\text{12 }}\Omega \) is connected in series with a cell of negligible internal resistance. The power dissipated in the resistor is \(P\). The resistor is replaced with a resistor of resistance \({\text{3.0 }}\Omega \). What is the power dissipated in this resistor?

A.     \(0.25{\text{ }}P\)

B.     \(P\)

C.     \(2.0{\text{ }}P\)

D.     \(4.0{\text{ }}P\)

D

A proton is accelerated from rest through a potential difference of 1000 V. What is the potential difference through which an alpha particle must be accelerated to gain the same kinetic energy as the accelerated proton?

A. 4000 V
B. 2000 V
C. 500 V
D. 250 V

C

B was the most popular response, presumably as the candidates were thinking ‘twice the charge, twice the potential difference’. A moment’s back checking, however, would show that this would lead to an alpha particle with four times the energy of the proton; therefore the correct response must be C.

In the circuit shown, the fixed resistor has a value of 3 Ω and the variable resistor can be varied between 0 Ω and 9 Ω.

The power supply has an emf of 12 V and negligible internal resistance. What is the difference between the maximum and minimum values of voltage V across the 3 Ω resistor?

A. 3 V

B. 6 V

C. 9 V

D. 12 V

C

The diagram shows two equal and opposite charges that are fixed in place.

At which points is the net electric field directed to the right?

A.  X and Y only

B.  Z and Y only

C.  X and Z only

D.  X, Y and Z

C

A wire carrying a current \(I\) is at right angles to a uniform magnetic field of strength B. A magnetic force F is exerted on the wire. Which force acts when the same wire is placed at right angles to a uniform magnetic field of strength 2B when the current is \(\frac{I}{4}\)?

A. \(\frac{F}{4}\)

B. \(\frac{F}{2}\)

C. F 

D. 2F

B

A –5µC charge and a +10µC charge are a fixed distance apart.

Where can the electric field be zero? 

A. position I only 
B. position II only 
C. position III only 
D. positions I, II and III

C

Three positive point charges of equal magnitude are held at the corners X, Y and Z of a right-angled triangle. The point P is at the midpoint of XY. Which of the arrows shows the direction of the electric field at point P?

B

An electron enters the vacuum between two oppositely charged plates with velocity \(v\). The electron is followed by an alpha particle moving with the same initial velocity as the electron. A uniform magnetic field is directed out of the plane of the paper.

The electron’s path is undeflected. The path of the alpha particle will be

A.     deflected out of the plane of the paper.

B.     undeflected.

C.     deflected upward.

D.     deflected downward.

B

A surprising number of students were confused by this question, with the evidence being that many were simply guessing. Crossing an electric and a magnetic field is the basis of selecting the velocity of charged particles as can be readily seen by equating \(Bqv\) to \(qE\). The charge cancels which means that if the electron is undeflected then the alpha particle will also be undeflected.

A liquid that contains negative charge carriers is flowing through a square pipe with sides A, B, C and D. A magnetic field acts in the direction shown across the pipe.

On which side of the pipe does negative charge accumulate?

A

An electron enters the region between two charged parallel plates initially moving parallel to the plates.

The electromagnetic force acting on the electron

A.     causes the electron to decrease its horizontal speed.

B.     causes the electron to increase its horizontal speed.

C.     is parallel to the field lines and in the opposite direction to them.

D.     is perpendicular to the field direction.

C

Two resistors, made of the same material, are connected in series to a battery. The length of resistor X is twice that of resistor Y, and X has twice the cross-sectional area of Y.

Which of the following gives \(\frac{{{\text{resistance of X}}}}{{{\text{resistance of Y}}}}\)?

A.     \(\frac{1}{4}\)

B.     \(\frac{1}{2}\)

C.     1

D.     4

C

A \( + 3{\text{ C}}\) charge and a \( - 4{\text{ C}}\) charge are a distance \(x\) apart. P is a distance \(x\) from the \( + 3{\text{ C}}\) charge on the straight line joining the charges.

What is the magnitude of the electric field strength at P?

A.     \(\frac{1}{{\pi {\varepsilon _0}{x^2}}}\)

B.     \(\frac{1}{{2\pi {\varepsilon _0}{x^2}}}\)

C.     \(\frac{1}{{4\pi {\varepsilon _0}{x^2}}}\)

D.     \(\frac{1}{{7\pi {\varepsilon _0}{x^2}}}\)

B

Although it is convenient to use k in the equation for coulombic attraction, candidates need to be able to unpack this as \(\frac{1}{{4\pi {\varepsilon _0}}}\).

What is the definition of electric current?

A. The ratio of potential difference across a component to the resistance of the component

B. The power delivered by a battery per unit potential difference

C. The rate of flow of electric charge

D. The energy per unit charge dissipated in a power supply

C

The magnetic field produced by a current in a straight wire is in

A. the same direction as the current.
B. the opposite direction to the current.
C. the same plane as the wire.
D. any plane perpendicular to the wire.

D

Which of the following will not give rise to a magnetic field?

A. A moving electron
B. A moving neutron
C. A proton and electron moving away from each other
D. A proton and electron moving towards each other

B

One electronvolt is equal to

A. 1.6×10⁻¹⁹ C.
B. 1.6×10⁻¹⁹ J.
C. 1.6×10⁻¹⁹ V.
D. 1.6×10⁻¹⁹ W.

B

An electron passes the north pole of a bar magnet as shown below.

What is the direction of the magnetic force on the electron?

A. Into the page
B. Out of the page
C. To the left
D. To the right

B

Two electrodes, separated by a distance d, in a vacuum are maintained at a constant potential difference. An electron, accelerated from one electrode to the other, gains kinetic energy E_k.

The distance between the electrodes is now changed to \(\frac{1}{3}\)d.

What is the gain in kinetic energy of an electron that is accelerated from one electrode to the other?

A battery of internal resistance 2 Ω is connected to an external resistance of 10 Ω. The current is 0.5 A.

What is the emf of the battery?

A. 1.0 V
B. 5.0 V
C. 6.0 V
D. 24.0 V

C

A battery of emf 6.0V is connected to a 2.0Ω resistor. The current in the circuit is 2.0A. The internal resistance of the battery is

A. zero.

B. 1.0 Ω.

C. 3.0 Ω.

D. 4.0 Ω.

B

Coulomb’s law refers to electric charges that are

A. on any charged objects.
B. charged hollow spheres.
C. charged solid spheres.
D. point charges.

D

An electric circuit consists of three identical resistors of resistance R connected to a cell of emf ε and negligible internal resistance.

What is the magnitude of the current in the cell?

A. \(\frac{\varepsilon }{{3R}}\)

B. \(\frac{{2\varepsilon }}{{3R}}\)

C. \(\frac{{3\varepsilon }}{{2R}}\)

D. \(\frac{{3\varepsilon }}{R}\)

B

Three resistors of resistance \(R\) are connected in parallel across a cell of electromotive force (emf) \(V\) that has a negligible internal resistance. What is the rate at which the cell supplies energy?

A.     \(\frac{{{V^2}}}{{3R}}\)

B.     \(\frac{{{V^2}}}{{9R}}\)

C.     \(\frac{{9{V^2}}}{R}\)

D.     \(\frac{{3{V^2}}}{R}\)

D

The diagram shows two long wires X and Y carrying identical currents in the same direction.

The direction of the force experienced by Y is

A. to the left.
B. to the right.
C. into the plane of the page.
D. out of the plane of the page.

A

A copper wire with length L and radius r has a resistance R.

What is the radius of a copper wire with length \(\frac{L}{2}\) and resistance R?

A. 2r

B. \(\sqrt 2 r\)

C. \(\frac{r}{{\sqrt 2}}\)

D. \(\frac{r}{2}\)

C

The ampere is defined in terms of

A. power dissipated in a wire of known length, cross-sectional area and resistivity.

B. potential difference across a resistance of known value.

C. number of electrons flowing past a point in a circuit in a given time.

D. force per unit length between parallel current-carrying conductors.

D

The majority of candidates chose the number of electrons flowing past a point in a given time
as the definition of the ampere when the correct answer is in terms of a force between parallel
currents.

An electron has a kinetic energy of 4.8×10^–10J. What is the equivalent value of this kinetic energy?

A. 3.0 eV
B. 3.0 keV
C. 3.0 MeV
D. 3.0 GeV

D

A cell is connected in series with a resistor and supplies a current of 4.0 A for a time of 500 s. During this time, 1.5 kJ of energy is dissipated in the cell and 2.5 kJ of energy is dissipated in the resistor.

What is the emf of the cell?

A.  0.50 V

B.  0.75 V

C.  1.5 V

D.  2.0 V

D

Which of the following is a statement of Ohm’s law?

A. The resistance of a conductor is constant.

B. The current in a conductor is inversely proportional to the potential difference across the conductor provided the temperature is constant.

C. The resistance of a conductor is constant provided that the temperature is constant.

D. The current in a conductor is proportional to the potential difference across it.

C

A cylindrical conductor of length \(l\), diameter \(D\) and resistivity \(\rho \) has resistance \(R\). A different cylindrical conductor of resistivity \(2\rho \), length \(2l\) and diameter \(2D\) has a resistance

A.     \(2R\)

B.     \(R\)

C.     \(\frac{R}{2}\)

D.     \(\frac{R}{4}\)

B

An electron is moving parallel to a straight current-carrying wire. The direction of conventional current in the wire and the direction of motion of the electron are the same. In which direction is the magnetic force on the electron?

D

The conventional current is opposite in direction to the electron flow. So here we have essentially anti-parallel currents and the candidates should know that such currents keep well away from each other, ie they repel, leaving D as the correct response.

A resistor X of resistance R is made of wire of length L and cross-sectional area A. Resistor Y is made of the same material but has a length 4L and a cross-sectional area 2A. X and Y are connected in series. What is the total resistance of the combination?

A. 1.5R
B. 2R
C. 3R
D. 9R

C

A cylindrical resistor of volume V and length l has resistance R. The resistor has a uniform circular cross-section. What is the resistivity of the material from which the resistor is made?

A. \(\frac{V}{{R{l^2}}}\)

B. \(\frac{{{V^{\rm{2}}}R}}{l}\)

C. \(\frac{{VR}}{{{l^2}}}\)

D. \(\frac{{{V^2}}}{{Rl}}\)

C

Two \(6{\text{ }}\Omega \) resistors are connected in series with a 6 V cell. A student incorrectly connects an ammeter and a voltmeter as shown below.

The readings on the ammeter and on the voltmeter are

B

The responses to this question indicated that many candidates were unfamiliar with circuit electricity, a topic which is suitable for teaching from a practical perspective. An ideal voltmeter would have a very high (infinite) resistance.

A circuit contains a cell of electromotive force (emf) 9.0 V and internal resistance 1.0 Ω together with a resistor of resistance 4.0 Ω as shown. The ammeter is ideal. XY is a connecting wire.

What is the reading of the ammeter?

A.  0 A

B.  1.8 A

C.  9.0 A

D.  11 A

C

Which of the following is the SI unit of gravitational field strength?

A. N
B. N m
C. Nkg^–1
D. Nm²kg^–2

C

An electron travelling in the direction shown by the arrow X, enters a region of uniform magnetic field. It leaves the region of field in the direction shown by the arrow Y.

The direction of the magnetic field is

A.     in the direction of X.

B.     into the plane of the paper.

C.     in the opposite direction to X.

D.     out of the plane of the paper.

D

Three wires, P, Q and R, carry equal currents directed into the plane of the paper.

Which arrow correctly identifies the direction of the magnetic force on wire P?

A. W
B. X
C. Y
D. Z

B

The candidates were not sure of how to tackle this. At some stage in their course, however, they should have seen wires carrying a current in the same direction, attracting each other; in which case this question is trivial.

Kirchhoff’s laws are applied to the circuit shown.

What is the equation for the dotted loop?

A. 0 = 3I₂ + 4I₃

B. 0 = 4I₃ − 3I₂

C. 6 = 2I₁ + 3I₂ + 4I₃

D. 6 = 3I₂ + 4I₃

B

The graph shows the variation of current with potential difference for a filament lamp.

What is the resistance of the filament when the potential difference across it is 6.0 V?
A.  0.5 mΩ
B.  1.5 mΩ
C.  670 Ω
D.  2000 Ω

C

Two resistors of resistance 10 Ω and 20 Ω are connected in parallel to a cell of negligible internal resistance.

The energy dissipated in the 10 Ω resistor in one second is Q. What is the energy dissipated in one second in the 20 Ω resistor?

A. \(\frac{Q}{4}\)
B. \(\frac{Q}{2}\)
C. 2Q
D. 4Q

B

With reference to internal energy conversion and ability to be recharged, what are the characteristics of a primary cell?

B

A circuit consists of a cell of electromotive force (emf) 6.0V and negligible internal resistance connected to two resistors of 4.0Ω.

A

B

A cell of emf 4V and negligible internal resistance is connected to three resistors as shown. Two resistors of resistance 2Ω are connected in parallel and are in series with a resistor of resistance 1Ω.

What power is dissipated in one of the 2Ω resistors and in the whole circuit?

D

Each of the resistors in the arrangements below has resistance R. Each arrangement is connected, in turn, to a power supply of constant emf and negligible internal resistance. In which arrangement is the current in the power supply greatest?

C

A cell is connected in series with a 2.0Ω resistor and a switch. The voltmeter is connected across the cell and reads 12V when the switch is open and 8.0V when the switch is closed.

What is the internal resistance of the cell?

A. 1.0 Ω
B. 2.0 Ω
C. 3.0 Ω
D. 4.0 Ω

A

An electrical circuit is shown with loop X and junction Y.

What is the correct expression of Kirchhoff’s circuit laws for loop X and junction Y?

A

Four resistors are connected as shown.

What is the total resistance between X and Y?

A. 3 Ω

B. 4 Ω

C. 6 Ω

D. 24 Ω

A

Three parallel wires, X, Y and Z, carry equal currents into the page.

Which arrow represents the direction of the magnetic force on wire Z?

C

This question dealt with electric potential, a topic that is not part of the SL syllabus. The
question was therefore deleted. The examination team apologizes for the logistical error of
including this HL question in the SL paper as well.

An electron is travelling in a region of uniform magnetic field. At the instant shown, the electron is moving parallel to the field direction.

The magnetic force on the electron is

A. upwards.

B. downwards.

C. to the right.

D. zero.

D

A cell with an emf of 2.0 V and negligible internal resistance is connected across a 1.00 m length of uniform resistance wire XY. The free end of the flying lead can be connected to any position on the wire.

What is the voltmeter reading when the flying lead is connected 0.25m from end X?

A. 0.00 V
B. 0.50 V
C. 1.50 V
D. 2.00 V

B

Two pulses are travelling towards each other.

What is a possible pulse shape when the pulses overlap?

A

Each of the resistors in the circuit has a resistance of 2.0 Ω. The cell has an emf of 3.0 V and negligible internal resistance. The ammeter has negligible resistance.

What is the ammeter reading?

A. 0.4 A
B. 0.5 A
C. 1.5 A
D. 2.0 A

C

Point P is at the same distance from two charges of equal magnitude and opposite sign.

What is the direction of the electric field at point P?

A

The graph shows the variation of current I in a device with potential difference V across it. 

C

Which of the following gives the resistances of an ideal ammeter and an ideal voltmeter?

B

A wire has variable cross-sectional area. The cross-sectional area at Y is double that at X.

At X, the current in the wire is I and the electron drift speed is v. What is the current and the electron drift speed at Y?

B

Three parallel wires, X, Y and Z, carry equal currents. The currents in X and Z are directed into the page. The current in Y is directed out of the page.

Which arrow shows the direction of the magnetic force experienced by wire Z?

A

Which of the following is the best representation of the electric field lines around a negatively charged metal sphere?

B

The diagram shows a circuit used to investigate internal resistance of a cell.

The variable resistor R is adjusted and the values of potential difference V across the cell and current I are recorded. Which graph shows the variation of V with I?

B

An ideal ammeter is used to measure the current in a resistor. Which of the following gives the resistance of an ideal ammeter and the way it is connected to the resistor?

D

Which diagram represents the pattern of electric field lines of two small positive point charges held at the positions shown?

B

A battery of emf 12 V and negligible internal resistance is connected to a resistor of constant resistance 6 Ω, an ideal ammeter and an ideal voltmeter.

What is the reading on the ammeter and on the voltmeter?

D

A long, straight, current-carrying wire is placed between a pair of magnets as shown. What is the direction of the force on the wire?

C

A

Three identical filament lamps W, X and Y are connected in the circuit as shown. The cell has negligible internal resistance.

When the switch is closed, all the lamps light. Which of the following correctly describes what happens to the brightness of lamp W and lamp Y when the switch is opened?

C

Three identical filament lamps, X, Y and Z, are connected as shown to a battery of negligible internal resistance.

The filament of lamp X breaks. Which of the following correctly describes the change in brightness of lamp Y and of lamp Z?

C

A lamp is connected to an electric cell and it lights at its working voltage. The lamp is then connected to the same cell in a circuit with an ideal ammeter and an ideal voltmeter. Which circuit allows the lamp to light at the original brightness?

B

Which of the following is the correct way of connecting an ammeter and of connecting a voltmeter in a circuit designed to measure the characteristics of a thermistor?

C