DP Physics Questionbank

Electrical power output is produced by several alternating current (ac) generators which use transformers to deliver energy to the national electricity grid.

The following data are available. Root mean square (rms) values are given.

(i) Calculate the current output by the transformer to the grid. Give your answer to an appropriate number of significant figures.

(ii) Electrical energy is often delivered across large distances at 330 kV. Identify the main advantage of using this very high potential difference.

In an alternating current (ac) generator, a square coil ABCD rotates in a magnetic field.

The ends of the coil are connected to slip rings and brushes. The plane of the coil is shown at the instant when it is parallel to the magnetic field. Only one coil is shown for clarity.

The following data are available.

(i) Explain, with reference to the diagram, how the rotation of the generator produces an electromotive force (emf ) between the brushes.

(ii) Calculate, for the position in the diagram, the magnitude of the instantaneous emf generated by a single wire between A and B of the coil.

(iii) Hence, calculate the total instantaneous peak emf between the brushes.

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?

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

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 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.

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?

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

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

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 magnetic flux $\Phi$ in a coil with time $t$.

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

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 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.

Calculate the distance between the plates.

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?

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

The input voltage is 240 V. Calculate the output voltage.

Three conducting loops, X, Y and Z, are moving with the same speed from a region of zero magnetic field to a region of uniform non-zero magnetic field.

Which loop(s) has/have the largest induced electromotive force (emf) at the instant when the loops enter the magnetic field?

A. Z only

B. Y only

C. Y and Z only

D. X and Y only

The use of alternating current (ac) in a transformer gives rise to energy losses. State how eddy current loss is minimized in the transformer.

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

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. $\frac{2BAN}{t}$

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 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.  $32 \text{W}$

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 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.

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.  $4$

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

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

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.

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

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

The secondary coil of an alternating current (ac) transformer is connected to two diodes as shown.

Which graph shows the variation with time of the potential difference V_XY between X and Y?

The capacitance of the capacitor is 22 mF. Calculate the energy stored in the capacitor when it is fully charged.

A direct current (dc) of 5A dissipates a power P in a resistor. Which peak value of the alternating current (ac) will dissipate an average power P in the same resistor?

A.  5A

B.  $\frac{5}{2}\text{A}$

C.  $\frac{5}{\sqrt{2}}\text{A}$

D.  $\text{5}\sqrt{2}\text{A}$

The resistance of the wire is 8.0 Ω. Determine the time taken for the capacitor to discharge through the resistance wire. Assume that the capacitor is completely discharged when the potential difference across it has fallen to 0.24 V.

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 $\frac{\ln 2}{RC}$.

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.

Calculate the maximum charge Q₀ stored in the capacitor.

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?

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.

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

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.  $\frac{1}{G\times I}$

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.

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

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

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.

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

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

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

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?

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

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

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

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

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.

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

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

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

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.  $8P$

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 $XX\mathit{\text{'}}$

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.

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

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

Calculate in J, the energy stored in the system.

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

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 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.  $I\sqrt{2}$

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

Calculate the change in the energy stored in the capacitor.

Calculate the root mean square (rms) current in each cable.

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 %

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

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

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?

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