Topic 11: Electromagnetic induction

Calculate the distance between the plates.

The plane of a coil is positioned at right angles to a magnetic field of flux density B. The coil has N turns, each of area A. The coil is rotated through 180˚ in time t.

What is the magnitude of the induced emf?

A. $\frac{BA}{t}$

B. $\frac{2BA}{t}$

C. $\frac{BAN}{t}$

D. $\frac{2BAN}{t}$

The plane of a coil is positioned at right angles to a magnetic field of flux density B. The coil has N turns, each of area A. The coil is rotated through 180˚ in time t.

What is the magnitude of the induced emf?

A. $\frac{BA}{t}$

B. $\frac{2BA}{t}$

C. $\frac{BAN}{t}$

D. $\frac{2BAN}{t}$

The ratio $\frac{\text{number of primary turns}}{\text{number of secondary turns}}$ for a transformer is 2.5.

The primary coil of the transformer draws a current of 0.25 A from a 200 V alternating current (ac) supply. The current in the secondary coil is 0.5 A. What is the efficiency of the transformer?

A. 20 %

B. 50 %

C. 80 %

D. 100 %

The ratio $\frac{\text{number of primary turns}}{\text{number of secondary turns}}$ for a transformer is 2.5.

The primary coil of the transformer draws a current of 0.25 A from a 200 V alternating current (ac) supply. The current in the secondary coil is 0.5 A. What is the efficiency of the transformer?

A. 20 %

B. 50 %

C. 80 %

D. 100 %

An alternating current (ac) generator produces a peak emf E₀ and periodic time T. What are the peak emf and periodic time when the frequency of rotation is doubled?

An alternating current (ac) generator produces a peak emf E₀ and periodic time T. What are the peak emf and periodic time when the frequency of rotation is doubled?

Six identical capacitors, each of value C, are connected as shown.

What is the total capacitance?

A. $\frac{C}{6}$

B. $\frac{2C}{3}$

C. $\frac{3C}{3}$

D. 6C

Six identical capacitors, each of value C, are connected as shown.

What is the total capacitance?

A. $\frac{C}{6}$

B. $\frac{2C}{3}$

C. $\frac{3C}{3}$

D. 6C

Calculate the distance between the plates.

Calculate the distance between the plates.

The capacitor is connected to a 16 V cell as shown.

Calculate the magnitude and the sign of the charge on plate A when the capacitor is fully charged.

The capacitor is connected to a 16 V cell as shown.

Calculate the magnitude and the sign of the charge on plate A when the capacitor is fully charged.

The capacitor is connected to a 16 V cell as shown.

Calculate the magnitude and the sign of the charge on plate A when the capacitor is fully charged.

The capacitor is fully charged and the space between the plates is then filled with a dielectric of permittivity ε = 3.0ε₀.

Explain whether the magnitude of the charge on plate A increases, decreases or stays constant.

The capacitor is fully charged and the space between the plates is then filled with a dielectric of permittivity ε = 3.0ε₀.

Explain whether the magnitude of the charge on plate A increases, decreases or stays constant.

The capacitor is fully charged and the space between the plates is then filled with a dielectric of permittivity ε = 3.0ε₀.

Explain whether the magnitude of the charge on plate A increases, decreases or stays constant.

In a different circuit, a transformer is connected to an alternating current (ac) supply.

The transformer has 100 turns in the primary coil and 1200 turns in the secondary coil. The peak value of the voltage of the ac supply is 220 V. Determine the root mean square (rms) value of the output voltage.

In a different circuit, a transformer is connected to an alternating current (ac) supply.

The transformer has 100 turns in the primary coil and 1200 turns in the secondary coil. The peak value of the voltage of the ac supply is 220 V. Determine the root mean square (rms) value of the output voltage.

Show that the capacitance of this arrangement is C = 6.6 × 10^–7 F.

In a different circuit, a transformer is connected to an alternating current (ac) supply.

The transformer has 100 turns in the primary coil and 1200 turns in the secondary coil. The peak value of the voltage of the ac supply is 220 V. Determine the root mean square (rms) value of the output voltage.

Describe the use of transformers in electrical power distribution.

Show that the capacitance of this arrangement is C = 6.6 × 10^–7 F.

Show that the capacitance of this arrangement is C = 6.6 × 10^–7 F.

Describe the use of transformers in electrical power distribution.

The graph shows the power dissipated in a resistor of 100 Ω when connected to an alternating current (ac) power supply of root mean square voltage (V_rms) 60 V.

What are the frequency of the ac power supply and the average power dissipated in the resistor?

Calculate in V, the potential difference between the thundercloud and the Earth’s surface.

Describe the use of transformers in electrical power distribution.

Calculate in V, the potential difference between the thundercloud and the Earth’s surface.

Calculate in V, the potential difference between the thundercloud and the Earth’s surface.

The graph shows the power dissipated in a resistor of 100 Ω when connected to an alternating current (ac) power supply of root mean square voltage (V_rms) 60 V.

What are the frequency of the ac power supply and the average power dissipated in the resistor?

A ring of area S is in a uniform magnetic field X. Initially the magnetic field is perpendicular to the plane of the ring. The ring is rotated by 180° about the axis in time T.

What is the average induced emf in the ring?

A.   0

B.   $\frac{XS}{2T}$

C.   $\frac{XS}{T}$

D.   $\frac{2XS}{T}$

A ring of area S is in a uniform magnetic field X. Initially the magnetic field is perpendicular to the plane of the ring. The ring is rotated by 180° about the axis in time T.

What is the average induced emf in the ring?

A.   0

B.   $\frac{XS}{2T}$

C.   $\frac{XS}{T}$

D.   $\frac{2XS}{T}$

Calculate in J, the energy stored in the system.

Calculate in J, the energy stored in the system.

Calculate in J, the energy stored in the system.

Show that about –11 C of charge is delivered to the Earth’s surface.

Show that about –11 C of charge is delivered to the Earth’s surface.

Show that about –11 C of charge is delivered to the Earth’s surface.

State one assumption that needs to be made so that the Earth-thundercloud system may be modelled by a parallel plate capacitor.

State one assumption that needs to be made so that the Earth-thundercloud system may be modelled by a parallel plate capacitor.

State one assumption that needs to be made so that the Earth-thundercloud system may be modelled by a parallel plate capacitor.

The motor can transfer one-third of the electrical energy stored in the capacitor into gravitational potential energy of the mass. Determine the maximum height through which a mass of 45 g can be raised.

The motor can transfer one-third of the electrical energy stored in the capacitor into gravitational potential energy of the mass. Determine the maximum height through which a mass of 45 g can be raised.

The motor can transfer one-third of the electrical energy stored in the capacitor into gravitational potential energy of the mass. Determine the maximum height through which a mass of 45 g can be raised.

The graph shows the variation of the peak output power P with time of an alternating current (ac) generator.

Which graph shows the variation of the peak output power with time when the frequency of rotation is decreased?

The graph shows the variation of the peak output power P with time of an alternating current (ac) generator.

Which graph shows the variation of the peak output power with time when the frequency of rotation is decreased?

Determine the peak current in the primary coil when operating with the maximum number of lamps.

A current of 1.0 × 10^–3A flows in the primary coil of a step-up transformer. The number of turns in the primary coil is N_p and the number of turns in the secondary coil is N_s. One coil has 1000 times more turns than the other coil.

What is $\frac{N_{\text{p}}}{N_{\text{s}}}$ and what is the current in the secondary coil for this transformer?

Determine the peak current in the primary coil when operating with the maximum number of lamps.

A current of 1.0 × 10^–3A flows in the primary coil of a step-up transformer. The number of turns in the primary coil is N_p and the number of turns in the secondary coil is N_s. One coil has 1000 times more turns than the other coil.

What is $\frac{N_{\text{p}}}{N_{\text{s}}}$ and what is the current in the secondary coil for this transformer?

Four identical capacitors of capacitance X are connected as shown in the diagram.

What is the effective capacitance between P and Q?

A.   $\frac{\text{X}}{3}$

B.   X

C.   $\frac{\text{4X}}{3}$

D.   4X

Determine the peak current in the primary coil when operating with the maximum number of lamps.

Four identical capacitors of capacitance X are connected as shown in the diagram.

What is the effective capacitance between P and Q?

A.   $\frac{\text{X}}{3}$

B.   X

C.   $\frac{\text{4X}}{3}$

D.   4X

The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.

The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.

Calculate the energy stored in the capacitor.

Calculate the total length of aluminium foil that the student will require.

Calculate the total length of aluminium foil that the student will require.

Calculate the total length of aluminium foil that the student will require.

The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.

The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.

Calculate the energy stored in the capacitor.

The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.

The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.

Calculate the energy stored in the capacitor.

Calculate the change in the energy stored in the capacitor.

Calculate the change in the energy stored in the capacitor.

Calculate the change in the energy stored in the capacitor.

The resistor R in the circuit has a resistance of 1.2 kΩ. Calculate the time taken for the charge on the capacitor to fall to 50 % of its fully charged value.

The resistor R in the circuit has a resistance of 1.2 kΩ. Calculate the time taken for the charge on the capacitor to fall to 50 % of its fully charged value.

The resistor R in the circuit has a resistance of 1.2 kΩ. Calculate the time taken for the charge on the capacitor to fall to 50 % of its fully charged value.

The graph below shows the variation with time of the magnetic flux through a coil.

Which of the following gives three times for which the magnitude of the induced emf is a maximum?

A. 0, $\frac{T}{4}$, $\frac{T}{2}$

B. 0, $\frac{T}{2}$, T

C. 0, $\frac{T}{4}$, T

D. $\frac{T}{4}$, $\frac{T}{2}$, $\frac{3T}{4}$

The graph below shows the variation with time of the magnetic flux through a coil.

Which of the following gives three times for which the magnitude of the induced emf is a maximum?

A. 0, $\frac{T}{4}$, $\frac{T}{2}$

B. 0, $\frac{T}{2}$, T

C. 0, $\frac{T}{4}$, T

D. $\frac{T}{4}$, $\frac{T}{2}$, $\frac{3T}{4}$

Suggest one change to the discharge circuit, apart from changes to the coil, that will increase the maximum induced emf in the coil.

Three identical capacitors are connected in series. The total capacitance of the arrangement is $\frac{1}{9}$mF. The three capacitors are then connected in parallel. What is the capacitance of the parallel arrangement?

A. $\frac{1}{3}$mF   

B. 1 mF

C. 3 mF

D. 81 mF

Three identical capacitors are connected in series. The total capacitance of the arrangement is $\frac{1}{9}$mF. The three capacitors are then connected in parallel. What is the capacitance of the parallel arrangement?

A. $\frac{1}{3}$mF   

B. 1 mF

C. 3 mF

D. 81 mF

A transformer with 600 turns in the primary coil is used to change an alternating root mean square (rms) potential difference of 240 V_rms to 12 V_rms.

When connected to the secondary coil, a lamp labelled “120 W, 12 V” lights normally. The current in the primary coil is 0.60 A when the lamp is lit.

What are the number of secondary turns and the efficiency of the transformer?

Suggest one change to the discharge circuit, apart from changes to the coil, that will increase the maximum induced emf in the coil.

Suggest one change to the discharge circuit, apart from changes to the coil, that will increase the maximum induced emf in the coil.

The circuit diagram shows a capacitor that is charged by the battery after the switch is connected to terminal X. The cell has emf V and internal resistance r. After the switch is connected to terminal Y the capacitor discharges through the resistor of resistance R.

What is the nature of the current and magnitude of the initial current in the resistor after the switch is connected to terminal Y?

The circuit diagram shows a capacitor that is charged by the battery after the switch is connected to terminal X. The cell has emf V and internal resistance r. After the switch is connected to terminal Y the capacitor discharges through the resistor of resistance R.

What is the nature of the current and magnitude of the initial current in the resistor after the switch is connected to terminal Y?

A transformer with 600 turns in the primary coil is used to change an alternating root mean square (rms) potential difference of 240 V_rms to 12 V_rms.

When connected to the secondary coil, a lamp labelled “120 W, 12 V” lights normally. The current in the primary coil is 0.60 A when the lamp is lit.

What are the number of secondary turns and the efficiency of the transformer?

Calculate, in J, the energy stored in X with the switch S open.

Calculate, in J, the energy stored in X with the switch S open.

Calculate, in J, the energy stored in X with the switch S open.

Calculate the final charge on X and the final charge on Y.

Calculate the final charge on X and the final charge on Y.

Calculate the final charge on X and the final charge on Y.

Calculate the final total energy, in J, stored in X and Y.

Calculate the final total energy, in J, stored in X and Y.

Calculate the final total energy, in J, stored in X and Y.

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

Power $P$ is dissipated in a resistor of resistance $R$ when there is a direct current $I$ in the resistor.

What is the average power dissipation in a resistance $\frac{R}{2}$ when the alternating root-mean-square (rms) current in the resistor is $2I$?

A.  $P$

B.  $2P$

C.  $4P$

D.  $8P$

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

Power $P$ is dissipated in a resistor of resistance $R$ when there is a direct current $I$ in the resistor.

What is the average power dissipation in a resistance $\frac{R}{2}$ when the alternating root-mean-square (rms) current in the resistor is $2I$?

A.  $P$

B.  $2P$

C.  $4P$

D.  $8P$

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

Explain, by reference to Faraday’s law of induction, how an electromotive force (emf) is induced in the coil.

A rectangular coil rotates at a constant angular velocity. At the instant shown, the plane of the coil is at right angles to the line $ZZ\mathit{\text{'}}$. A uniform magnetic field acts in the direction $ZZ\mathit{\text{'}}$.

What rotation of the coil about a specified axis will produce the graph of electromotive force (emf) $E$ against time $t$?

A.  Through $\frac{\mathrm{\pi }}{2}$ about $ZZ\mathit{\text{'}}$

B.  Through $\mathrm{\pi }$ about $YY\mathit{\text{'}}$

C.  Through $\frac{\mathrm{\pi }}{2}$ about $XX\mathit{\text{'}}$

D.  Through $\mathrm{\pi }$ about $XX\mathit{\text{'}}$

A rectangular coil rotates at a constant angular velocity. At the instant shown, the plane of the coil is at right angles to the line $ZZ\mathit{\text{'}}$. A uniform magnetic field acts in the direction $ZZ\mathit{\text{'}}$.

What rotation of the coil about a specified axis will produce the graph of electromotive force (emf) $E$ against time $t$?

A.  Through $\frac{\mathrm{\pi }}{2}$ about $ZZ\mathit{\text{'}}$

B.  Through $\mathrm{\pi }$ about $YY\mathit{\text{'}}$

C.  Through $\frac{\mathrm{\pi }}{2}$ about $XX\mathit{\text{'}}$

D.  Through $\mathrm{\pi }$ about $XX\mathit{\text{'}}$

A capacitor of capacitance $C$ has initial charge $Q$. The capacitor is discharged through a resistor of resistance $R$. The potential difference $V$ across the capacitor varies with time.

What is true for this capacitor?

A.  After time $\frac{RC}{2}$ the potential difference across the capacitor is halved.

B.  The capacitor discharges more quickly when the resistance is changed to $2R$.

C.  The rate of change of charge on the capacitor is proportional to $V$.

D.  The time for the capacitor to lose half its charge is $\frac{\ln 2}{RC}$.

A capacitor of capacitance $C$ has initial charge $Q$. The capacitor is discharged through a resistor of resistance $R$. The potential difference $V$ across the capacitor varies with time.

What is true for this capacitor?

A.  After time $\frac{RC}{2}$ the potential difference across the capacitor is halved.

B.  The capacitor discharges more quickly when the resistance is changed to $2R$.

C.  The rate of change of charge on the capacitor is proportional to $V$.

D.  The time for the capacitor to lose half its charge is $\frac{\ln 2}{RC}$.

Explain, by reference to Faraday’s law of induction, how an electromotive force (emf) is induced in the coil.

Explain, by reference to Faraday’s law of induction, how an electromotive force (emf) is induced in the coil.

The average power output of the generator is $8.5\times {10}^5 \mathrm{W}$. Calculate the root mean square (rms) value of the generator output current.

The average power output of the generator is $8.5\times {10}^5 \mathrm{W}$. Calculate the root mean square (rms) value of the generator output current.

The average power output of the generator is $8.5\times {10}^5 \mathrm{W}$. Calculate the root mean square (rms) value of the generator output current.

The voltage output from the generator is stepped up before transmission to the consumer. Estimate the factor by which voltage has to be stepped up in order to reduce power loss in the transmission line by a factor of $2.5\times {10}^2$.

The voltage output from the generator is stepped up before transmission to the consumer. Estimate the factor by which voltage has to be stepped up in order to reduce power loss in the transmission line by a factor of $2.5\times {10}^2$.

The voltage output from the generator is stepped up before transmission to the consumer. Estimate the factor by which voltage has to be stepped up in order to reduce power loss in the transmission line by a factor of $2.5\times {10}^2$.

The frequency of the generator is doubled with no other changes being made. Draw, on the axes, the variation with time of the voltage output of the generator.

The frequency of the generator is doubled with no other changes being made. Draw, on the axes, the variation with time of the voltage output of the generator.

The frequency of the generator is doubled with no other changes being made. Draw, on the axes, the variation with time of the voltage output of the generator.

The primary coil has 3300 turns. Calculate the number of turns on the secondary coil.

Show that the maximum energy stored by the capacitor is about 160 J.

Show that the maximum energy stored by the capacitor is about 160 J.

The primary coil has 3300 turns. Calculate the number of turns on the secondary coil.

The primary coil has 3300 turns. Calculate the number of turns on the secondary coil.

Show that the maximum energy stored by the capacitor is about 160 J.

Calculate the maximum charge Q₀ stored in the capacitor.

Calculate the current in the primary of the transformer assuming that it is ideal.

A resistor designed for use in a direct current (dc) circuit is labelled “50 W, 2 Ω”. The resistor is connected in series with an alternating current (ac) power supply of peak potential difference 10 V. What is the average power dissipated by the resistor in the ac circuit?

A. 25 W

B. 35 W

C. 50 W

D. 100 W

Calculate the maximum charge Q₀ stored in the capacitor.

Calculate the maximum charge Q₀ stored in the capacitor.

A resistor designed for use in a direct current (dc) circuit is labelled “50 W, 2 Ω”. The resistor is connected in series with an alternating current (ac) power supply of peak potential difference 10 V. What is the average power dissipated by the resistor in the ac circuit?

A. 25 W

B. 35 W

C. 50 W

D. 100 W

Calculate the current in the primary of the transformer assuming that it is ideal.

Calculate the current in the primary of the transformer assuming that it is ideal.

Flux leakage is one reason why a transformer may not be ideal. Explain the effect of flux leakage on the transformer.

A capacitor of capacitance X is connected to a power supply of voltage V. At time t = 0, the capacitor is disconnected from the supply and discharged through a resistor of resistance R. What is the variation with time of the charge on the capacitor?

$\text{A. }\frac{X}{V}{e}^{-RXt}$

$\text{B. }\frac{X}{V}{e}^{-\frac{t}{RX}}$

$\text{C. }XV{e}^{-RXt}$

$\text{D. }XV{e}^{-\frac{t}{RX}}$

A capacitor of capacitance X is connected to a power supply of voltage V. At time t = 0, the capacitor is disconnected from the supply and discharged through a resistor of resistance R. What is the variation with time of the charge on the capacitor?

$\text{A. }\frac{X}{V}{e}^{-RXt}$

$\text{B. }\frac{X}{V}{e}^{-\frac{t}{RX}}$

$\text{C. }XV{e}^{-RXt}$

$\text{D. }XV{e}^{-\frac{t}{RX}}$

Flux leakage is one reason why a transformer may not be ideal. Explain the effect of flux leakage on the transformer.

Flux leakage is one reason why a transformer may not be ideal. Explain the effect of flux leakage on the transformer.

Show that the charge remaining in the capacitor after a time equal to one time constant $\tau$ of the circuit will be 0.37 Q₀.

The graph shows the variation of an alternating current with time in a $4.0 \text{Ω}$ resistor.

What is the average power dissipated in the resistor?

A.  $4 \text{W}$

B.  $8 \text{W}$

C.  $16 \text{W}$

D.  $32 \text{W}$

Show that the charge remaining in the capacitor after a time equal to one time constant $\tau$ of the circuit will be 0.37 Q₀.

Show that the charge remaining in the capacitor after a time equal to one time constant $\tau$ of the circuit will be 0.37 Q₀.

The graph shows the variation with time of the charge in the capacitor as it is being discharged through the heart.

Determine the electrical resistance of the closed circuit with the switch in position B.

The graph shows the variation of an alternating current with time in a $4.0 \text{Ω}$ resistor.

What is the average power dissipated in the resistor?

A.  $4 \text{W}$

B.  $8 \text{W}$

C.  $16 \text{W}$

D.  $32 \text{W}$

A magnet connected to a spring oscillates above a solenoid with a 240 turn coil as shown.

The graph below shows the variation with time $t$ of the emf across the solenoid with the period, $T$, of the system shown.

The spring is replaced with one that allows the magnet to oscillate with a higher frequency. Which graph shows the new variation with time $t$ of the current $I$ in the resistor for this new set-up?

The graph shows the variation with time of the charge in the capacitor as it is being discharged through the heart.

Determine the electrical resistance of the closed circuit with the switch in position B.

The graph shows the variation with time of the charge in the capacitor as it is being discharged through the heart.

Determine the electrical resistance of the closed circuit with the switch in position B.

A magnet connected to a spring oscillates above a solenoid with a 240 turn coil as shown.

The graph below shows the variation with time $t$ of the emf across the solenoid with the period, $T$, of the system shown.

The spring is replaced with one that allows the magnet to oscillate with a higher frequency. Which graph shows the new variation with time $t$ of the current $I$ in the resistor for this new set-up?

A capacitor is charged with a constant current $I$. The graph shows the variation of potential difference $V$ across the capacitor with time $t$. The gradient of the graph is $G$. What is the capacitance of the capacitor?

A.  $\frac{I}{G}$

B.  $\frac{G}{I}$

C.  $G\times I$

D.  $\frac{1}{G\times I}$

Show that the speed of the loop is 20 cm s⁻¹.

A capacitor is charged with a constant current $I$. The graph shows the variation of potential difference $V$ across the capacitor with time $t$. The gradient of the graph is $G$. What is the capacitance of the capacitor?

A.  $\frac{I}{G}$

B.  $\frac{G}{I}$

C.  $G\times I$

D.  $\frac{1}{G\times I}$

Show that the speed of the loop is 20 cm s⁻¹.

Show that the speed of the loop is 20 cm s⁻¹.

Sketch, on the axes, a graph to show the variation with time of the magnetic flux linkage $\Phi$ in the loop.

The root mean square (rms) current in the primary coil of an ideal transformer is 2.0 A. The rms voltage in the secondary coil is 50 V. The average power transferred from the secondary coil is 20 W.

What is $\frac{N_p}{N_s}$ and what is the average power transferred from the primary coil?

The root mean square (rms) current in the primary coil of an ideal transformer is 2.0 A. The rms voltage in the secondary coil is 50 V. The average power transferred from the secondary coil is 20 W.

What is $\frac{N_p}{N_s}$ and what is the average power transferred from the primary coil?

The switch is then connected to Y and C discharges through the 20 MΩ resistor. The voltage V_c drops to 50 % of its initial value in 5.0 s. Determine the capacitance of C.

Sketch, on the axes, a graph to show the variation with time of the magnetic flux linkage $\Phi$ in the loop.

The switch is then connected to Y and C discharges through the 20 MΩ resistor. The voltage V_c drops to 50 % of its initial value in 5.0 s. Determine the capacitance of C.

The switch is then connected to Y and C discharges through the 20 MΩ resistor. The voltage V_c drops to 50 % of its initial value in 5.0 s. Determine the capacitance of C.

Two initially uncharged capacitors X and Y are connected in series to a cell as shown.

What is $\frac{\text{voltage across X}}{\text{voltage across Y}}$?

A.  $\frac{1}{2}$

B.  $1$

C.  $2$

D.  $4$

Sketch, on the axes, a graph to show the variation with time of the magnetic flux linkage $\Phi$ in the loop.

Sketch, on the axes, a graph to show the variation with time of the magnitude of the emf induced in the loop.

Two initially uncharged capacitors X and Y are connected in series to a cell as shown.

What is $\frac{\text{voltage across X}}{\text{voltage across Y}}$?

A.  $\frac{1}{2}$

B.  $1$

C.  $2$

D.  $4$

Sketch, on the axes, a graph to show the variation with time of the magnitude of the emf induced in the loop.

Sketch, on the axes, a graph to show the variation with time of the magnitude of the emf induced in the loop.

There are 85 turns of wire in the loop. Calculate the maximum induced emf in the loop.

There are 85 turns of wire in the loop. Calculate the maximum induced emf in the loop.

There are 85 turns of wire in the loop. Calculate the maximum induced emf in the loop.

State the fundamental SI unit for your answer to (a)(i).

The graph shows the variation of magnetic flux $\Phi$ in a coil with time $t$.

What represents the variation with time of the induced emf $\epsilon$ across the coil?

State the fundamental SI unit for your answer to (a)(i).

The graph shows the variation of magnetic flux $\Phi$ in a coil with time $t$.

What represents the variation with time of the induced emf $\epsilon$ across the coil?

State the fundamental SI unit for your answer to (a)(i).

A direct current $I$ in a lamp dissipates power P. What root mean square (rms) value of an alternating current dissipates average power P through the same lamp?

A.  $\frac{I}{2}$

B.  $\frac{I}{\sqrt{2}}$

C.  $I$

D.  $I\sqrt{2}$

A direct current $I$ in a lamp dissipates power P. What root mean square (rms) value of an alternating current dissipates average power P through the same lamp?

A.  $\frac{I}{2}$

B.  $\frac{I}{\sqrt{2}}$

C.  $I$

D.  $I\sqrt{2}$

Show that the charge stored on C₁ is about 0.04 mC.

Show that the charge stored on C₁ is about 0.04 mC.

Show that the charge stored on C₁ is about 0.04 mC.

The arrangement shows four diodes connected to an alternating current (ac) supply. The output is connected to an external circuit.

What is the output to the external circuit?

A.  Full-wave rectified current

B.  Half-wave rectified current

C.  Constant non-zero current

D.  Zero current

The arrangement shows four diodes connected to an alternating current (ac) supply. The output is connected to an external circuit.

What is the output to the external circuit?

A.  Full-wave rectified current

B.  Half-wave rectified current

C.  Constant non-zero current

D.  Zero current

Calculate the energy transferred from capacitor C₁.

Calculate the energy transferred from capacitor C₁.

Calculate the energy transferred from capacitor C₁.

Explain why the energy gained by capacitor C₂ differs from your answer in (b)(i).

Explain why the energy gained by capacitor C₂ differs from your answer in (b)(i).

Explain why the energy gained by capacitor C₂ differs from your answer in (b)(i).

Calculate the energy stored in the capacitor.

A parallel-plate capacitor is fully charged using a battery.

The capacitor has a capacitance C and a charge Q. The plates X and Y of the capacitor are a distance d apart. Edge effects are negligible.

Three statements about the fully charged capacitor are:

I.    The electric field strength between the plates is $\frac{Q}{Cd}$.

II.   The electric field lines are at right angles to the plates.

III.  The equipotential surfaces are parallel to the plates.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Determine the average emf induced across coil Y in the first 3.0 ms.

Determine the average emf induced across coil Y in the first 3.0 ms.

Determine the average emf induced across coil Y in the first 3.0 ms.

Calculate the energy stored in the capacitor.

Calculate the energy stored in the capacitor.

Explain the change, if any, to the potential difference between the plates.

A parallel-plate capacitor is fully charged using a battery.

The capacitor has a capacitance C and a charge Q. The plates X and Y of the capacitor are a distance d apart. Edge effects are negligible.

Three statements about the fully charged capacitor are:

I.    The electric field strength between the plates is $\frac{Q}{Cd}$.

II.   The electric field lines are at right angles to the plates.

III.  The equipotential surfaces are parallel to the plates.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Explain the change, if any, to the potential difference between the plates.

Explain the change, if any, to the potential difference between the plates.

Determine the work required to increase the separation of the plates.

Determine the work required to increase the separation of the plates.

Determine the work required to increase the separation of the plates.

Draw, on the axes, a graph to show the variation with time of the current in the resistor.

Draw, on the axes, a graph to show the variation with time of the current in the resistor.

Draw, on the axes, a graph to show the variation with time of the current in the resistor.

A diode bridge rectification circuit is often modified by adding a capacitor in parallel with the output (load) resistance.

Describe the reason for this modification.

A diode bridge rectification circuit is often modified by adding a capacitor in parallel with the output (load) resistance.

Describe the reason for this modification.

A student states three facts about the time constant of a resistor-capacitor series circuit.

I.   It is the time required for the capacitor to be charged through the resistor to a voltage of 0.632 V from an initial value of zero, where V is the voltage of the source.

II.  It is the time required for the capacitor to be discharged through the resistor to a voltage of 0.632 V, where V is the initial voltage of the capacitor.

III. It is the product of the resistance of the resistor and the capacitance of the capacitor.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A diode bridge rectification circuit is often modified by adding a capacitor in parallel with the output (load) resistance.

Describe the reason for this modification.

A student states three facts about the time constant of a resistor-capacitor series circuit.

I.   It is the time required for the capacitor to be charged through the resistor to a voltage of 0.632 V from an initial value of zero, where V is the voltage of the source.

II.  It is the time required for the capacitor to be discharged through the resistor to a voltage of 0.632 V, where V is the initial voltage of the capacitor.

III. It is the product of the resistance of the resistor and the capacitance of the capacitor.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

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.

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.

Wire XY moves perpendicular to a magnetic field in the direction shown.

The graph shows the variation with time of the displacement of XY.

What is the graph of the electromotive force (emf) ε induced across XY?

Wire XY moves perpendicular to a magnetic field in the direction shown.

The graph shows the variation with time of the displacement of XY.

What is the graph of the electromotive force (emf) ε induced across XY?