Topic 5: Electricity and magnetism

Two wires, X and Y, are made from the same metal. The wires are connected in series. The radius of X is twice that of Y. The carrier drift speed in X is v_X and in Y it is v_Y.

What is the value of the ratio $\frac{{\text{v}}_{\text{X}}}{{\text{v}}_{\text{Y}}}$?

A. 0.25

B. 0.50

C. 2.00

D. 4.00

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

Calculate the drift speed v of the electrons in the conductor in cm s^–1. State your answer to an appropriate number of significant figures.

An ion of charge +Q moves vertically upwards through a small distance s in a uniform vertical electric field. The electric field has a strength E and its direction is shown in the diagram.

What is the electric potential difference between the initial and final position of the ion?

A.     $\frac{EQ}{s}$

B.     EQs

C.     Es

D.     $\frac{E}{s}$

Calculate the drift speed v of the electrons in the conductor in cm s^–1.

Determine the electric field strength E.

Show that $\frac{v}{E}=\frac{1}{ne\rho }$.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

Calculate, in A, the average current during the discharge.

Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression

$$v=\sqrt{\frac{k{e}^2}{m_{\text{e}}r}}$$

where k is the Coulomb constant.

Two copper wires X and Y are connected in series. The diameter of Y is double that of X. The drift speed in X is v. What is the drift speed in Y?

A.   $\frac{v}{4}$

B.   $\frac{v}{2}$

C.   2v

D.   4v

Two point charges Q₁ and Q₂ are one metre apart. The graph shows the variation of electric potential V with distance $x$ from Q₁.

What is $\frac{Q_1}{Q_2}$?

A.   $\frac{1}{16}$

B.   $\frac{1}{4}$

C.   4

D.   16

Outline why the ions are likely to spread out.

Outline why the ions are likely to spread out.

Show that the time taken for the battery to discharge is about 3 × 10³ s.

A particle with a charge ne is accelerated through a potential difference V.

What is the magnitude of the work done on the particle?

A. $eV$

B. $neV$

C. $\frac{nV}{e}$

D. $\frac{eV}{n}$

Two parallel plates are a distance apart with a potential difference between them. A point charge moves from the negatively charged plate to the positively charged plate. The charge gains kinetic energy W. The distance between the plates is doubled and the potential difference between them is halved. What is the kinetic energy gained by an identical charge moving between these plates?

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

B. W

C. 2W

D. 4W

The force acting between two point charges is $F$ when the separation of the charges is $x$. What is the force between the charges when the separation is increased to $3x$?

A. $\frac{F}{3}$

B. $\frac{F}{3x^2}$

C. $\frac{F}{9}$

D. $\frac{F}{9x^2}$

Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10⁸ N C^–1.

Calculate the magnitude of the initial acceleration of the electron.

A metal wire has $n$ free charge carriers per unit volume. The charge on the carrier is $q$. What additional quantity is needed to determine the current per unit area in the wire?

A.  Cross-sectional area of the wire

B.  Drift speed of charge carriers

C.  Potential difference across the wire

D.  Resistivity of the metal

Calculate the electric potential difference between points A and B.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

The centre of the ball, still carrying a charge of $1.2\times {10}^{-6} \text{C}$, is now placed $0.40 \text{m}$ from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.

P is the point on the line joining the charges where the electric field strength is zero.
The distance PQ is $0.22 \text{m}$.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

A charge +Q and a charge −2Q are a distance 3x apart. Point P is on the line joining the charges, at a distance x from +Q.

The magnitude of the electric field produced at P by the charge +Q alone is $E$.

What is the total electric field at P?

A.  $\frac{E}{2}$ to the right

B.  $\frac{E}{2}$ to the left

C.  $\frac{3E}{2}$ to the right

D.  $\frac{3E}{2}$ to the left

The work done to move a particle of charge 0.25 μC from one point in an electric field to another is 4.5 μJ. Calculate the magnitude of the potential difference between the two points.

Determine the force on Q at the instant it is released.

Show that the magnitude of the resultant electric field at P is 3 MN C⁻¹

P and Q are two opposite point charges. The force F acting on P due to Q and the electric field strength E at P are shown.

Which diagram shows the force on Q due to P and the electric field strength at Q?

Two cylinders, X and Y, made from the same material, are connected in series.

The cross-sectional area of Y is twice that of X. The drift speed of the electrons in X is $v_{\text{X}}$ and in Y it is $v_{\text{Y}}$.

What is the ratio $\frac{v_{\text{X}}}{v_{\text{Y}}}$?

A.  4

B.  2

C.  1

D.  $\frac{1}{2}$

Deduce whether the motion of Z is simple harmonic.

Four particles, two of charge +Q and two of charge −Q, are positioned on the $x$-axis as shown. A particle P with a positive charge is placed on the $y$-axis. What is the direction of the net electrostatic force on this particle?

Wire $\text{X}$ and wire $\text{Y}$ are connected in series in a circuit. Wire $\text{X}$ has three times the radius and one third the charge carrier density of wire $\text{Y}$.

What is $\frac{\text{drift speed in X}}{\text{drift speed in Y}}$?

A.  $\frac{1}{9}$

B.  $\frac{1}{3}$

C.  $1$

D.  $3$

Two copper wires of equal lengths but different diameters are used to connect a cell to a load. Wire 1 has a diameter M, wire 2 has a diameter 2M. The electron drift velocities in wires 1 and 2 are $v_1$ and $v_2$.

What is $\frac{v_2}{v_1}$?

A.  $4$

B.  $2$

C.  $\frac{1}{2}$

D.  $\frac{1}{4}$

An electric field is established between two electrodes separated by distance d, held at a potential difference of V. A charged particle in this field experiences a force F.

What is the charge on the particle?

A.  $\frac{d}{FV}$

B.  $\frac{FV}{d}$

C.  $\frac{V}{Fd}$

D.  $\frac{Fd}{V}$

Show that the time taken for the battery to discharge is about 3 × 10³ s.

Show that the time taken for the battery to discharge is about 3 × 10³ s.

A particle with a charge ne is accelerated through a potential difference V.

What is the magnitude of the work done on the particle?

A. $eV$

B. $neV$

C. $\frac{nV}{e}$

D. $\frac{eV}{n}$

Two parallel plates are a distance apart with a potential difference between them. A point charge moves from the negatively charged plate to the positively charged plate. The charge gains kinetic energy W. The distance between the plates is doubled and the potential difference between them is halved. What is the kinetic energy gained by an identical charge moving between these plates?

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

B. W

C. 2W

D. 4W

The force acting between two point charges is $F$ when the separation of the charges is $x$. What is the force between the charges when the separation is increased to $3x$?

A. $\frac{F}{3}$

B. $\frac{F}{3x^2}$

C. $\frac{F}{9}$

D. $\frac{F}{9x^2}$

Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10⁸ N C^–1.

Calculate the magnitude of the initial acceleration of the electron.

Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10⁸ N C^–1.

Calculate the magnitude of the initial acceleration of the electron.

A metal wire has $n$ free charge carriers per unit volume. The charge on the carrier is $q$. What additional quantity is needed to determine the current per unit area in the wire?

A.  Cross-sectional area of the wire

B.  Drift speed of charge carriers

C.  Potential difference across the wire

D.  Resistivity of the metal

Calculate the electric potential difference between points A and B.

Calculate the electric potential difference between points A and B.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

The centre of the ball, still carrying a charge of $1.2\times {10}^{-6} \text{C}$, is now placed $0.40 \text{m}$ from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.

P is the point on the line joining the charges where the electric field strength is zero.
The distance PQ is $0.22 \text{m}$.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

The centre of the ball, still carrying a charge of $1.2\times {10}^{-6} \text{C}$, is now placed $0.40 \text{m}$ from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.

P is the point on the line joining the charges where the electric field strength is zero.
The distance PQ is $0.22 \text{m}$.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

A charge +Q and a charge −2Q are a distance 3x apart. Point P is on the line joining the charges, at a distance x from +Q.

The magnitude of the electric field produced at P by the charge +Q alone is $E$.

What is the total electric field at P?

A.  $\frac{E}{2}$ to the right

B.  $\frac{E}{2}$ to the left

C.  $\frac{3E}{2}$ to the right

D.  $\frac{3E}{2}$ to the left

The work done to move a particle of charge 0.25 μC from one point in an electric field to another is 4.5 μJ. Calculate the magnitude of the potential difference between the two points.

Determine the force on Q at the instant it is released.

The work done to move a particle of charge 0.25 μC from one point in an electric field to another is 4.5 μJ. Calculate the magnitude of the potential difference between the two points.

Determine the force on Q at the instant it is released.

Show that the magnitude of the resultant electric field at P is 3 MN C⁻¹

Show that the magnitude of the resultant electric field at P is 3 MN C⁻¹

P and Q are two opposite point charges. The force F acting on P due to Q and the electric field strength E at P are shown.

Which diagram shows the force on Q due to P and the electric field strength at Q?

Two cylinders, X and Y, made from the same material, are connected in series.

The cross-sectional area of Y is twice that of X. The drift speed of the electrons in X is $v_{\text{X}}$ and in Y it is $v_{\text{Y}}$.

What is the ratio $\frac{v_{\text{X}}}{v_{\text{Y}}}$?

A.  4

B.  2

C.  1

D.  $\frac{1}{2}$

Deduce whether the motion of Z is simple harmonic.

Deduce whether the motion of Z is simple harmonic.

Four particles, two of charge +Q and two of charge −Q, are positioned on the $x$-axis as shown. A particle P with a positive charge is placed on the $y$-axis. What is the direction of the net electrostatic force on this particle?

Wire $\text{X}$ and wire $\text{Y}$ are connected in series in a circuit. Wire $\text{X}$ has three times the radius and one third the charge carrier density of wire $\text{Y}$.

What is $\frac{\text{drift speed in X}}{\text{drift speed in Y}}$?

A.  $\frac{1}{9}$

B.  $\frac{1}{3}$

C.  $1$

D.  $3$

Two copper wires of equal lengths but different diameters are used to connect a cell to a load. Wire 1 has a diameter M, wire 2 has a diameter 2M. The electron drift velocities in wires 1 and 2 are $v_1$ and $v_2$.

What is $\frac{v_2}{v_1}$?

A.  $4$

B.  $2$

C.  $\frac{1}{2}$

D.  $\frac{1}{4}$

An electric field is established between two electrodes separated by distance d, held at a potential difference of V. A charged particle in this field experiences a force F.

What is the charge on the particle?

A.  $\frac{d}{FV}$

B.  $\frac{FV}{d}$

C.  $\frac{V}{Fd}$

D.  $\frac{Fd}{V}$

Two wires, X and Y, are made from the same metal. The wires are connected in series. The radius of X is twice that of Y. The carrier drift speed in X is v_X and in Y it is v_Y.

What is the value of the ratio $\frac{{\text{v}}_{\text{X}}}{{\text{v}}_{\text{Y}}}$?

A. 0.25

B. 0.50

C. 2.00

D. 4.00

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

Calculate the drift speed v of the electrons in the conductor in cm s^–1. State your answer to an appropriate number of significant figures.

Calculate the drift speed v of the electrons in the conductor in cm s^–1. State your answer to an appropriate number of significant figures.

An ion of charge +Q moves vertically upwards through a small distance s in a uniform vertical electric field. The electric field has a strength E and its direction is shown in the diagram.

What is the electric potential difference between the initial and final position of the ion?

A.     $\frac{EQ}{s}$

B.     EQs

C.     Es

D.     $\frac{E}{s}$

Calculate the drift speed v of the electrons in the conductor in cm s^–1.

Determine the electric field strength E.

Show that $\frac{v}{E}=\frac{1}{ne\rho }$.

Calculate the drift speed v of the electrons in the conductor in cm s^–1.

Determine the electric field strength E.

Show that $\frac{v}{E}=\frac{1}{ne\rho }$.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

Calculate, in A, the average current during the discharge.

Calculate, in A, the average current during the discharge.

Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression

$$v=\sqrt{\frac{k{e}^2}{m_{\text{e}}r}}$$

where k is the Coulomb constant.

Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression

$$v=\sqrt{\frac{k{e}^2}{m_{\text{e}}r}}$$

where k is the Coulomb constant.

Two copper wires X and Y are connected in series. The diameter of Y is double that of X. The drift speed in X is v. What is the drift speed in Y?

A.   $\frac{v}{4}$

B.   $\frac{v}{2}$

C.   2v

D.   4v

Two point charges Q₁ and Q₂ are one metre apart. The graph shows the variation of electric potential V with distance $x$ from Q₁.

What is $\frac{Q_1}{Q_2}$?

A.   $\frac{1}{16}$

B.   $\frac{1}{4}$

C.   4

D.   16

Outline why the ions are likely to spread out.

Outline why the ions are likely to spread out.

Outline why the ions are likely to spread out.

Outline why the ions are likely to spread out.

The resistance of the carbon film is 82 Ω. The resistivity of carbon is 4.1 x 10^–5 Ω m. Calculate the length l of the film.

The film must dissipate a power less than 1500 W from each square metre of its surface to avoid damage. Calculate the maximum allowable current for the resistor.

The current direction is now changed so that charge flows vertically through the film.

Deduce, without calculation, the change in the resistance.

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

Calculate the resistance of the conductor.

Show that the resistance of the wire AC is 28 Ω.

Determine E.

Calculate the resistance of the conductor.

Show that the resistance of the wire AC is 28 Ω.

Determine E.

Cell X is replaced by a second cell of identical emf E but with internal resistance 2.0 Ω. Comment on the length of AC for which the current in the second cell is zero.

A combination of four identical resistors each of resistance R are connected to a source of emf ε of negligible internal resistance. What is the current in the resistor X?

A.   $\frac{\epsilon }{5R}$

B.   $\frac{3\epsilon }{10R}$

C.   $\frac{2\epsilon }{5R}$

D.   $\frac{3\epsilon }{5R}$

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Calculate the internal resistance of one cell.

In an experiment to determine the resistivity of a material, a student measures the resistance of several wires made from the pure material. The wires have the same length but different diameters.

Which quantities should the student plot on the $x$-axis and the $y$-axis of a graph to obtain a straight line?

The switch S is initially open. Calculate the total power dissipated in the circuit.

The switch is now closed. Deduce the ratio $\frac{\text{power dissipated in Y with S open}}{\text{power dissipated in Y with S closed}}$.

Suggest why the answers to (a) and (b)(ii) are different.

The experiment is repeated using a wire made of the same material but of a larger diameter than the wire in part (a). On the axes in part (a), draw the graph for this second experiment.

An electric motor raises an object of weight $500 \mathrm{N}$ through a vertical distance of $3.0 \mathrm{m}$ in $1.5 \mathrm{s}$. The current in the electric motor is $10 \mathrm{A}$ at a potential difference of $200 \mathrm{V}$. What is the efficiency of the electric motor?

A.  $17 \%$

B.  $38 \%$

C.  $50 \%$

D.  $75 \%$

Four resistors of $4 \mathrm{\Omega }$ each are connected as shown.

What is the effective resistance between P and Q?

A.  $1.0 \mathrm{\Omega }$

B.  $2.4 \mathrm{\Omega }$

C.  $3.4 \mathrm{\Omega }$

D.  $4.0 \mathrm{\Omega }$

A cell of electromotive force (emf) $E$ and zero internal resistance is in the circuit shown.

What is correct for loop WXYUW?

A.  $E=3I_{1}R-I_{3}R$

B.  $E=I_{3}R-I_{2}R$

C.  $E=I_{3}R$

D.  $E=2I_{2}R-I_{3}R$

What is the relationship between the resistivity $\rho$ of a uniform wire, the radius $r$ of the wire and the length $l$ of the wire when its resistance is constant?

A.  $\rho \propto r^{2}l$

B.  $\rho \propto r{l}^2$

C.  $\rho \propto \frac{l}{r^2}$

D.  $\rho \propto \frac{r^2}{l}$

A power station generates $250 \mathrm{kW}$ of power at a potential difference of $25 \mathrm{kV}$. The energy is transmitted through cables of total resistance $4.0 \mathrm{\Omega }$.

What is the power loss in the cables?

A.  $0.04 \mathrm{kW}$

B.  $0.4 \mathrm{kW}$

C.  $4 \mathrm{kW}$

D.  $40 \mathrm{kW}$

Determine the resistance of the variable resistor.

Calculate the power dissipated in the circuit.

State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.

Describe, by reference to your answer for (c)(i), the advantage of the potential divider arrangement over the arrangement in (b).

Determine the resistance of the variable resistor.

Calculate the power dissipated in the circuit.

State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.

Slider S of the potential divider is positioned so that the ammeter reads $20 \text{mA}$. Explain, without further calculation, any difference in the power transferred by the potential divider arrangement over the arrangement in (b).

Show that each resistor has a resistance of about 30 Ω.

Determine the total resistance of the lamps when they are working normally.

The diagram shows two cylindrical wires, X and Y. Wire X has a length $l$, a diameter $d$, and a resistivity $\rho$. Wire Y has a length $2l$, a diameter of $\frac{d}{2}$and a resistivity of $\frac{\rho }{2}$.

What is $\frac{\text{resistance of X}}{\text{resistance of Y}}$?

A. 4

B. 2

C. 0.5

D. 0.25

Three identical resistors of resistance R are connected as shown to a battery with a potential difference of $12 \text{V}$ and an internal resistance of $\frac{\text{R}}{2}$. A voltmeter is connected across one of the resistors.

What is the reading on the voltmeter?

A. $3 \text{V}$

B. $4 \text{V}$

C. $6 \text{V}$

D. $8 \text{V}$

A circuit contains a variable resistor of maximum resistance R and a fixed resistor, also of resistance R, connected in series. The emf of the battery is $6.0 \text{V}$ and its internal resistance is negligible.

What are the initial and final voltmeter readings when the variable resistor is increased from an initial resistance of zero to a final resistance of R?

Two wires, $\text{X}$ and $\text{Y}$, are made of the same material and have equal length. The diameter of $\text{X}$ is twice that of $\text{Y}$.

What is $\frac{\text{resistance of X}}{\text{resistance of Y}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  $2$

D.  $4$

The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.

Show that the energy dissipated in the loop from t = 0 to t = 3.5 s is 0.13 J.

A circuit consists of a cell of emf E = 3.0 V and four resistors connected as shown. Resistors R₁ and R₄ are 1.0 Ω and resistors R₂ and R₃ are 2.0 Ω.

What is the voltmeter reading?

A.  0.50 V

B.  1.0 V

C.  1.5 V

D.  2.0 V

Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.

The voltmeter is used in another circuit that contains two secondary cells.

Cell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 V and an internal resistance of 2.0 Ω.

Calculate the reading on the voltmeter.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.

Calculate the reading on the voltmeter.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

Three identical resistors each of resistance R are connected with a variable resistor X as shown. X is initially set to R. The current in the cell is 0.60 A.

The cell has negligible internal resistance.

X is now set to zero. What is the current in the cell?

A.  0.45 A

B.  0.60 A

C.  0.90 A

D.  1.80 A

In the circuit shown, the battery has an emf of 12 V and negligible internal resistance. Three identical resistors are connected as shown. The resistors each have a resistance of 10 Ω.

The resistor L is removed. What is the change in potential at X?

A.  Increases by 2 V

B.  Decreases by 2 V

C.  Increases by 4 V

D.  Decreases by 4 V

Two cells are connected in parallel as shown below. Each cell has an emf of 5.0 V and an internal resistance of 2.0 Ω. The lamp has a resistance of 4.0 Ω. The ammeter is ideal.

What is the reading on the ammeter?

A.  1.0 A

B.  1.3 A

C.  2.0 A

D.  2.5 A

Calculate the potential difference across P. 

The voltmeter reads zero. Determine the resistance of S.

Deduce the resistance of this new cylinder when it has been reshaped.

Outline, without calculation, the change in the total power dissipated in Q and the new cylinder after it has been reshaped.

A cell of negligible internal resistance is connected to three identical resistors. The current in the cell is 3.0 A.

The resistors are now arranged in series.

What is the new current in the cell?

A.  1.0 A

B.  1.5 A

C.  3.0 A

D.  9.0 A

Determine the total power dissipated in the circuit.

Calculate, in mA, the current in the resistor.

Calculate the internal resistance of one cell.

Calculate the internal resistance of one cell.

In an experiment to determine the resistivity of a material, a student measures the resistance of several wires made from the pure material. The wires have the same length but different diameters.

Which quantities should the student plot on the $x$-axis and the $y$-axis of a graph to obtain a straight line?

The switch S is initially open. Calculate the total power dissipated in the circuit.

The switch is now closed. Deduce the ratio $\frac{\text{power dissipated in Y with S open}}{\text{power dissipated in Y with S closed}}$.

The switch S is initially open. Calculate the total power dissipated in the circuit.

The switch is now closed. Deduce the ratio $\frac{\text{power dissipated in Y with S open}}{\text{power dissipated in Y with S closed}}$.

Suggest why the answers to (a) and (b)(ii) are different.

Suggest why the answers to (a) and (b)(ii) are different.

The experiment is repeated using a wire made of the same material but of a larger diameter than the wire in part (a). On the axes in part (a), draw the graph for this second experiment.

The experiment is repeated using a wire made of the same material but of a larger diameter than the wire in part (a). On the axes in part (a), draw the graph for this second experiment.

An electric motor raises an object of weight $500 \mathrm{N}$ through a vertical distance of $3.0 \mathrm{m}$ in $1.5 \mathrm{s}$. The current in the electric motor is $10 \mathrm{A}$ at a potential difference of $200 \mathrm{V}$. What is the efficiency of the electric motor?

A.  $17 \%$

B.  $38 \%$

C.  $50 \%$

D.  $75 \%$

Four resistors of $4 \mathrm{\Omega }$ each are connected as shown.

What is the effective resistance between P and Q?

A.  $1.0 \mathrm{\Omega }$

B.  $2.4 \mathrm{\Omega }$

C.  $3.4 \mathrm{\Omega }$

D.  $4.0 \mathrm{\Omega }$

A cell of electromotive force (emf) $E$ and zero internal resistance is in the circuit shown.

What is correct for loop WXYUW?

A.  $E=3I_{1}R-I_{3}R$

B.  $E=I_{3}R-I_{2}R$

C.  $E=I_{3}R$

D.  $E=2I_{2}R-I_{3}R$

What is the relationship between the resistivity $\rho$ of a uniform wire, the radius $r$ of the wire and the length $l$ of the wire when its resistance is constant?

A.  $\rho \propto r^{2}l$

B.  $\rho \propto r{l}^2$

C.  $\rho \propto \frac{l}{r^2}$

D.  $\rho \propto \frac{r^2}{l}$

A power station generates $250 \mathrm{kW}$ of power at a potential difference of $25 \mathrm{kV}$. The energy is transmitted through cables of total resistance $4.0 \mathrm{\Omega }$.

What is the power loss in the cables?

A.  $0.04 \mathrm{kW}$

B.  $0.4 \mathrm{kW}$

C.  $4 \mathrm{kW}$

D.  $40 \mathrm{kW}$

Determine the resistance of the variable resistor.

Calculate the power dissipated in the circuit.

State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.

Describe, by reference to your answer for (c)(i), the advantage of the potential divider arrangement over the arrangement in (b).

Determine the resistance of the variable resistor.

Calculate the power dissipated in the circuit.

State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.

Describe, by reference to your answer for (c)(i), the advantage of the potential divider arrangement over the arrangement in (b).

Determine the resistance of the variable resistor.

Calculate the power dissipated in the circuit.

State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.

Slider S of the potential divider is positioned so that the ammeter reads $20 \text{mA}$. Explain, without further calculation, any difference in the power transferred by the potential divider arrangement over the arrangement in (b).

Determine the resistance of the variable resistor.

Calculate the power dissipated in the circuit.

State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.

Slider S of the potential divider is positioned so that the ammeter reads $20 \text{mA}$. Explain, without further calculation, any difference in the power transferred by the potential divider arrangement over the arrangement in (b).

Show that each resistor has a resistance of about 30 Ω.

Show that each resistor has a resistance of about 30 Ω.

Determine the total resistance of the lamps when they are working normally.

Determine the total resistance of the lamps when they are working normally.

The diagram shows two cylindrical wires, X and Y. Wire X has a length $l$, a diameter $d$, and a resistivity $\rho$. Wire Y has a length $2l$, a diameter of $\frac{d}{2}$and a resistivity of $\frac{\rho }{2}$.

What is $\frac{\text{resistance of X}}{\text{resistance of Y}}$?

A. 4

B. 2

C. 0.5

D. 0.25

Three identical resistors of resistance R are connected as shown to a battery with a potential difference of $12 \text{V}$ and an internal resistance of $\frac{\text{R}}{2}$. A voltmeter is connected across one of the resistors.

What is the reading on the voltmeter?

A. $3 \text{V}$

B. $4 \text{V}$

C. $6 \text{V}$

D. $8 \text{V}$

A circuit contains a variable resistor of maximum resistance R and a fixed resistor, also of resistance R, connected in series. The emf of the battery is $6.0 \text{V}$ and its internal resistance is negligible.

What are the initial and final voltmeter readings when the variable resistor is increased from an initial resistance of zero to a final resistance of R?

Two wires, $\text{X}$ and $\text{Y}$, are made of the same material and have equal length. The diameter of $\text{X}$ is twice that of $\text{Y}$.

What is $\frac{\text{resistance of X}}{\text{resistance of Y}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  $2$

D.  $4$

The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.

Show that the energy dissipated in the loop from t = 0 to t = 3.5 s is 0.13 J.

The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.

Show that the energy dissipated in the loop from t = 0 to t = 3.5 s is 0.13 J.

A circuit consists of a cell of emf E = 3.0 V and four resistors connected as shown. Resistors R₁ and R₄ are 1.0 Ω and resistors R₂ and R₃ are 2.0 Ω.

What is the voltmeter reading?

A.  0.50 V

B.  1.0 V

C.  1.5 V

D.  2.0 V

Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.

The voltmeter is used in another circuit that contains two secondary cells.

Cell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 V and an internal resistance of 2.0 Ω.

Calculate the reading on the voltmeter.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.

The voltmeter is used in another circuit that contains two secondary cells.

Cell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 V and an internal resistance of 2.0 Ω.

Calculate the reading on the voltmeter.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.

Calculate the reading on the voltmeter.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.

Calculate the reading on the voltmeter.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

Three identical resistors each of resistance R are connected with a variable resistor X as shown. X is initially set to R. The current in the cell is 0.60 A.

The cell has negligible internal resistance.

X is now set to zero. What is the current in the cell?

A.  0.45 A

B.  0.60 A

C.  0.90 A

D.  1.80 A

In the circuit shown, the battery has an emf of 12 V and negligible internal resistance. Three identical resistors are connected as shown. The resistors each have a resistance of 10 Ω.

The resistor L is removed. What is the change in potential at X?

A.  Increases by 2 V

B.  Decreases by 2 V

C.  Increases by 4 V

D.  Decreases by 4 V

Two cells are connected in parallel as shown below. Each cell has an emf of 5.0 V and an internal resistance of 2.0 Ω. The lamp has a resistance of 4.0 Ω. The ammeter is ideal.

What is the reading on the ammeter?

A.  1.0 A

B.  1.3 A

C.  2.0 A

D.  2.5 A

Calculate the potential difference across P. 

The voltmeter reads zero. Determine the resistance of S.

Deduce the resistance of this new cylinder when it has been reshaped.

Outline, without calculation, the change in the total power dissipated in Q and the new cylinder after it has been reshaped.

Calculate the potential difference across P. 

The voltmeter reads zero. Determine the resistance of S.

Deduce the resistance of this new cylinder when it has been reshaped.

Outline, without calculation, the change in the total power dissipated in Q and the new cylinder after it has been reshaped.

A cell of negligible internal resistance is connected to three identical resistors. The current in the cell is 3.0 A.

The resistors are now arranged in series.

What is the new current in the cell?

A.  1.0 A

B.  1.5 A

C.  3.0 A

D.  9.0 A

Determine the total power dissipated in the circuit.

Determine the total power dissipated in the circuit.

Calculate, in mA, the current in the resistor.

Calculate, in mA, the current in the resistor.

The resistance of the carbon film is 82 Ω. The resistivity of carbon is 4.1 x 10^–5 Ω m. Calculate the length l of the film.

The film must dissipate a power less than 1500 W from each square metre of its surface to avoid damage. Calculate the maximum allowable current for the resistor.

The current direction is now changed so that charge flows vertically through the film.

Deduce, without calculation, the change in the resistance.

The resistance of the carbon film is 82 Ω. The resistivity of carbon is 4.1 x 10^–5 Ω m. Calculate the length l of the film.

The film must dissipate a power less than 1500 W from each square metre of its surface to avoid damage. Calculate the maximum allowable current for the resistor.

The current direction is now changed so that charge flows vertically through the film.

Deduce, without calculation, the change in the resistance.

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

Calculate the resistance of the conductor.

Calculate the resistance of the conductor.

Show that the resistance of the wire AC is 28 Ω.

Determine E.

Show that the resistance of the wire AC is 28 Ω.

Determine E.

Calculate the resistance of the conductor.

Calculate the resistance of the conductor.

Show that the resistance of the wire AC is 28 Ω.

Determine E.

Cell X is replaced by a second cell of identical emf E but with internal resistance 2.0 Ω. Comment on the length of AC for which the current in the second cell is zero.

Show that the resistance of the wire AC is 28 Ω.

Determine E.

Cell X is replaced by a second cell of identical emf E but with internal resistance 2.0 Ω. Comment on the length of AC for which the current in the second cell is zero.

A combination of four identical resistors each of resistance R are connected to a source of emf ε of negligible internal resistance. What is the current in the resistor X?

A.   $\frac{\epsilon }{5R}$

B.   $\frac{3\epsilon }{10R}$

C.   $\frac{2\epsilon }{5R}$

D.   $\frac{3\epsilon }{5R}$

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.

Show that the gradient of the graph is equal to $\frac{1}{e}$.

State what is meant by the emf of a cell.

When an electric cell of negligible internal resistance is connected to a resistor of resistance 4R, the power dissipated in the resistor is P.

What is the power dissipated in a resistor of resistance value R when it is connected to the same cell?

A.     $\frac{P}{4}$

B.     P

C.     4P

D.     16P

State what is meant by the emf of a cell.

The switch S is initially open. Calculate the total power dissipated in the circuit.

The switch is now closed. $\text{Deduce the ratio }\frac{\text{power dissipated in Y with S open}}{\text{power dissipated in Y with S closed}}$.

Determine the internal resistance of the battery.

Calculate the emf of one cell.

An electrical power supply has an internal resistance. It supplies a direct current $I$ to an external circuit for a time $t$. What is the electromotive force (emf) of the power supply?

A.  $\frac{\mathrm{total} \mathrm{energy} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{whole} \mathrm{circuit}}{I\times t}$

B.  $\frac{\mathrm{total} \mathrm{power} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{whole} \mathrm{circuit}}{I\times t}$

C.  $\frac{\mathrm{total} \mathrm{energy} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{external} \mathrm{circuit}}{I\times t}$

D.  $\frac{\mathrm{total} \mathrm{power} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{external} \mathrm{circuit}}{I\times t}$

Explain why the output potential difference to the external circuit and the output emf of the photovoltaic cell are different.

Calculate the internal resistance of the photovoltaic cell for the maximum intensity condition using the model for the cell.

Three identical resistors of resistance R are connected as shown to a battery with a potential difference of $12 \text{V}$ and an internal resistance of $\frac{\text{R}}{2}$. A voltmeter is connected across one of the resistors.

What is the reading on the voltmeter?

A. $3 \text{V}$

B. $4 \text{V}$

C. $6 \text{V}$

D. $8 \text{V}$

Deduce the internal resistance of the cell.

Deduce the internal resistance of the cell.

Comment on the implications of your answer to (c)(i) for cell B.

Show that the internal resistance of the cell is about 0.7 Ω.

Show that the internal resistance of the cell is about 0.7 Ω.

Calculate the emf of the cell.

The switch S is initially open. Calculate the total power dissipated in the circuit.

The switch is now closed. $\text{Deduce the ratio }\frac{\text{power dissipated in Y with S open}}{\text{power dissipated in Y with S closed}}$.

The switch S is initially open. Calculate the total power dissipated in the circuit.

The switch is now closed. $\text{Deduce the ratio }\frac{\text{power dissipated in Y with S open}}{\text{power dissipated in Y with S closed}}$.

Determine the internal resistance of the battery.

Calculate the emf of one cell.

Determine the internal resistance of the battery.

Calculate the emf of one cell.

An electrical power supply has an internal resistance. It supplies a direct current $I$ to an external circuit for a time $t$. What is the electromotive force (emf) of the power supply?

A.  $\frac{\mathrm{total} \mathrm{energy} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{whole} \mathrm{circuit}}{I\times t}$

B.  $\frac{\mathrm{total} \mathrm{power} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{whole} \mathrm{circuit}}{I\times t}$

C.  $\frac{\mathrm{total} \mathrm{energy} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{external} \mathrm{circuit}}{I\times t}$

D.  $\frac{\mathrm{total} \mathrm{power} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{external} \mathrm{circuit}}{I\times t}$

Explain why the output potential difference to the external circuit and the output emf of the photovoltaic cell are different.

Calculate the internal resistance of the photovoltaic cell for the maximum intensity condition using the model for the cell.

Explain why the output potential difference to the external circuit and the output emf of the photovoltaic cell are different.

Calculate the internal resistance of the photovoltaic cell for the maximum intensity condition using the model for the cell.

Three identical resistors of resistance R are connected as shown to a battery with a potential difference of $12 \text{V}$ and an internal resistance of $\frac{\text{R}}{2}$. A voltmeter is connected across one of the resistors.

What is the reading on the voltmeter?

A. $3 \text{V}$

B. $4 \text{V}$

C. $6 \text{V}$

D. $8 \text{V}$

Deduce the internal resistance of the cell.

Deduce the internal resistance of the cell.

Deduce the internal resistance of the cell.

Comment on the implications of your answer to (c)(i) for cell B.

Deduce the internal resistance of the cell.

Comment on the implications of your answer to (c)(i) for cell B.

Show that the internal resistance of the cell is about 0.7 Ω.

Show that the internal resistance of the cell is about 0.7 Ω.

Show that the internal resistance of the cell is about 0.7 Ω.

Calculate the emf of the cell.

Show that the internal resistance of the cell is about 0.7 Ω.

Calculate the emf of the cell.

Show that the gradient of the graph is equal to $\frac{1}{e}$.

Show that the gradient of the graph is equal to $\frac{1}{e}$.

State what is meant by the emf of a cell.

State what is meant by the emf of a cell.

When an electric cell of negligible internal resistance is connected to a resistor of resistance 4R, the power dissipated in the resistor is P.

What is the power dissipated in a resistor of resistance value R when it is connected to the same cell?

A.     $\frac{P}{4}$

B.     P

C.     4P

D.     16P

State what is meant by the emf of a cell.

State what is meant by the emf of a cell.

State the direction of the magnetic field.

Calculate, in N, the magnitude of the magnetic force acting on the electron.

For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

A beam of negative ions flows in the plane of the page through the magnetic field due to two bar magnets.

What is the direction in which the negative ions will be deflected?

A. Out of the page $\odot$

B. Into the page X

C. Up the page ↑

D. Down the page ↓

The speed of the proton is 2.16 × 10⁶ m s^-1 and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

Show that the radius of the path is about 6 cm.

The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

An electron is accelerated from rest through a potential difference V.

What is the maximum speed of the electron?

A.  $\sqrt{\frac{2eV}{m_e}}$

B.  $\frac{eV}{m_e}$

C.  $\frac{2eV}{m_e}$

D.  $\sqrt{\frac{2V}{m_e}}$

Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

A beam of negative ions flows in the plane of the page through the magnetic field due to two bar magnets.

What is the direction in which the negative ions will be deflected?

A. Out of the page $\odot$

B. Into the page X

C. Up the page ↑

D. Down the page ↓

The speed of the proton is 2.16 × 10⁶ m s^-1 and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

The speed of the proton is 2.16 × 10⁶ m s^-1 and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

Show that the radius of the path is about 6 cm.

Show that the radius of the path is about 6 cm.

The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.

The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

An electron is accelerated from rest through a potential difference V.

What is the maximum speed of the electron?

A.  $\sqrt{\frac{2eV}{m_e}}$

B.  $\frac{eV}{m_e}$

C.  $\frac{2eV}{m_e}$

D.  $\sqrt{\frac{2V}{m_e}}$

Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.

Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.

State the direction of the magnetic field.

Calculate, in N, the magnitude of the magnetic force acting on the electron.

State the direction of the magnetic field.

Calculate, in N, the magnitude of the magnetic force acting on the electron.