Topic 11 Revision [129 marks]
1.
A ring of area S is in a uniform magnetic field X. Initially the magnetic field is
[1 mark]
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.
XS
2T
C.
XS
T
D.
2XS
T
Markscheme
D
Examiners report
[N/A]
The graph shows the variation of the peak output power P with time of an alternating
2.
The graph shows the variation of the peak output power P with time of an alternating
current (ac) generator.
[1 mark]
Which graph shows the variation of the peak output power with time when the frequency of
rotation is decreased?
Markscheme
C
Examiners report
[N/A]
A current of 1.0 × 10 –3 A flows in the primary coil of a step-up transformer. The number
3.
A current of 1.0 × 10 –3 A flows in the primary coil of a step-up transformer. The number [1 mark]
of turns in the primary coil is Np and the number of turns in the secondary coil is Ns.
One coil has 1000 times more turns than the other coil.
What is
Np
Ns
and what is the current in the secondary coil for this transformer?
Markscheme
A
Examiners report
[N/A]
4.
Four identical capacitors of capacitance X are connected as shown in the diagram.
What is the effective capacitance between P and Q?
X
3
A.
B. X
4X
3
C.
D. 4X
Markscheme
C
[1 mark]
Examiners report
[N/A]
A lighting system consists of two long metal rods with a potential difference maintained between
them. Identical lamps can be connected between the rods as required.
The following data are available for the lamps when at their working temperature.
Lamp specifications 24 V, 5.0 W
Power supply emf 24 V
Power supply maximum current 8.0 A
Length of each rod 12.5 m
Resistivity of rod metal 7.2 × 10–7 Ω m
5a. Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the
[3 marks]
minimum radius of each rod. Give your answer to an appropriate number of significant
figures.
Markscheme
ALTERNATIVE 1:
r = √ πR OR √ 7.2×π10×0.1×12.5 ✔
−7
ρl
r = 5.352 × 10 −3 ✔
5.4 × 10 −3 «m» ✔
For MP2 accept any SF
For MP3 accept only 2 SF
For MP3 accept ANY answer given to 2 SF
ALTERNATIVE 2:
A=
7.2×10−7×12.5
0.1
✔
r = 5.352 × 10−3 ✔
5.4 × 10−3 «m» ✔
For MP2 accept any SF
For MP3 accept only 2 SF
For MP3 accept ANY answer given to 2 SF
Examiners report
[N/A]
5b. Calculate the maximum number of lamps that can be connected between the
rods. Neglect the resistance of the rods.
[2 marks]
Markscheme
current in lamp =
5
24
«= 0.21» «A»
OR
n = 24 ×
8
5
✔
so «38.4 and therefore» 38 lamps ✔
Do not award ECF from MP1
Examiners report
[N/A]
5c. One advantage of this system is that if one lamp fails then the other lamps in the
[1 mark]
circuit remain lit. Outline one other electrical advantage of this system compared to one
in which the lamps are connected in series.
Markscheme
when adding more lamps in parallel the brightness stays the same ✔
when adding more lamps in parallel the pd across each remains the same/at the operating
value/24 V ✔
when adding more lamps in parallel the current through each remains the same ✔
lamps can be controlled independently ✔
the pd across each bulb is larger in parallel ✔
the current in each bulb is greater in parallel ✔
lamps will be brighter in parallel than in series ✔
In parallel the pd across the lamps will be the operating value/24 V ✔
Accept converse arguments for adding lamps in series:
when adding more lamps in series the brightness decreases
when adding more lamps in series the pd decreases
when adding more lamps in series the current decreases
lamps can’t be controlled independently
the pd across each bulb is smaller in series
the current in each bulb is smaller in series
in series the pd across the lamps will less than the operating value/24 V
Do not accept statements that only compare the overall resistance of the combination of
bulbs.
Examiners report
[N/A]
A step-down transformer is used to transfer energy to the two rods. The primary coil of this
A step-down transformer is used to transfer energy to the two rods. The primary coil of this
transformer is connected to an alternating mains supply that has an emf of root mean square
(rms) magnitude 240 V. The transformer is 95 % efficient.
5d. Outline how eddy currents reduce transformer efficiency.
[2 marks]
Markscheme
«as flux linkage change occurs in core, induced emfs appear so» current is induced ✔
induced currents give rise to resistive forces ✔
eddy currents cause thermal energy losses «in conducting core» ✔
power dissipated by eddy currents is drawn from the primary coil/reduces power delivered
to the secondary ✔
Examiners report
[N/A]
5e. Determine the peak current in the primary coil when operating with the maximum
number of lamps.
[4 marks]
Markscheme
power = 190 OR 192 «W» ✔
required power = 190 ×
so
200
240
100
95
«200 or 202 W» ✔
= 0.83 OR 0.84 «A rms» ✔
peak current = « 0.83 × √2 OR 0.84 × √2» = 1.2/1.3 «A» ✔
Examiners report
[N/A]
A small electric motor is used with a 12 mF capacitor and a battery in a school experiment.
When the switch is connected to X, the capacitor is charged using the battery. When the switch
is connected to Y, the capacitor fully discharges through the electric motor that raises a small
mass.
6a. The battery has an emf of 7.5 V. Determine the charge that flows through the
motor when the mass is raised.
Markscheme
charge stored on capacitor = 12 × 10 −3 × 7.5 = 0.09 «C» ✔
[1 mark]
Examiners report
[N/A]
6b. 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.
[2 marks]
Markscheme
energy stored in capacitor « 12 CV2 or
height = « 13 ×
0.338
9.81×4.5×10−2
1
QV
2
=»
1
2
× 12 × 10−3 × 7.52 «= 0.338 J» ✔
=» 0.25/0.26 «m»
Allow use of g = 10 m s −2 which gives 0.25 «m»
Examiners report
[N/A]
6c. An additional identical capacitor is connected in series with the first capacitor and
the charging and discharging processes are repeated. Comment on the effect this
change has on the height and time taken to raise the 45 g mass.
[3 marks]
Markscheme
C halved ✔
so energy stored is halved/reduced so rises «less than» half height ✔
discharge time/raise time less as RC halved/reduced ✔
Allow 6 mF
Examiners report
[N/A]
7.
Two identical circular coils are placed one below the other so that their planes are both [1 mark]
horizontal. The top coil is connected to a cell and a switch.
The switch is closed and then opened. What is the force between the coils when the switch is
closing and when the switch is opening?
Markscheme
C
Examiners report
[N/A]
The graph shows the variation with time t of the current I in the primary coil of an ideal
8.
The graph shows the variation with time t of the current I in the primary coil of an ideal [1 mark]
transformer.
The number of turns in the primary coil is 100 and the number of turns in the secondary coil is
200. Which graph shows the variation with time of the current in the secondary coil?
Markscheme
D
Examiners report
[N/A]
The diagram shows a diode bridge rectification circuit and a load resistor.
9.
The diagram shows a diode bridge rectification circuit and a load resistor.
[1 mark]
The input is a sinusoidal signal. Which of the following circuits will produce the most smoothed
output signal?
Markscheme
C
Examiners report
[N/A]
A parallel plate capacitor is connected to a cell of negligible internal resistance.
10. A parallel plate capacitor is connected to a cell of negligible internal resistance.
[1 mark]
The energy stored in the capacitor is 4 J and the electric field in between the plates is 100 N C –
1. The distance between the plates of the capacitor is doubled. What are the energy stored and
the electric field strength?
Markscheme
A
Examiners report
[N/A]
11. The current I flowing in loop A in a clockwise direction is increasing so as to induce a
current both in loops B and C. All three loops are on the same plane.
What is the direction of the induced currents in loop B and loop C?
Markscheme
C
[1 mark]
Examiners report
[N/A]
12. A rectangular flat coil moves at constant speed through a uniform magnetic field. The
direction of the field is into the plane of the paper.
[1 mark]
Which graph shows the variation with time t, of the induced emf ε in the coil as it moves from P
to Q?
Markscheme
A
Examiners report
[N/A]
The graph shows the power dissipated in a resistor of 100 Ω when connected to
13. 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 (Vrms) 60 V.
[1 mark]
What are the frequency of the ac power supply and the average power dissipated in the
resistor?
Markscheme
A
Examiners report
[N/A]
14. Three capacitors, each one with a capacitance C, are connected such that their
combined capacitance is 1.5C. How are they connected?
Markscheme
C
[1 mark]
Examiners report
[N/A]
A capacitor consists of two parallel square plates separated by a vacuum. The plates are 2.5 cm
× 2.5 cm squares. The capacitance of the capacitor is 4.3 pF.
15a. Calculate the distance between the plates.
Markscheme
d=«
8.85×10−12×0.0252
4.3×10−12
=» 1.3 × 10 –3 «m»
[1 mark]
Examiners report
[N/A]
The capacitor is connected to a 16 V cell as shown.
[1 mark]
15b. The capacitor is connected to a 16 V cell as shown.
[2 marks]
Calculate the magnitude and the sign of the charge on plate A when the capacitor is fully
charged.
Markscheme
6.9 × 10 –11 «C»
negative charge/sign
[2 marks]
Examiners report
[N/A]
15c. The capacitor is fully charged and the space between the plates is then filled with a
dielectric of permittivity ε = 3.0 ε0.
[2 marks]
Explain whether the magnitude of the charge on plate A increases, decreases or stays constant.
Markscheme
charge increases
because capacitance increases AND pd remains the same.
[2 marks]
Examiners report
[N/A]
15d. In a different circuit, a transformer is connected to an alternating current (ac) supply.
[3 marks]
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.
Markscheme
ALTERNATIVE 1
εs =
1200
100
× 220
= 2640 «V»
Vrms =
2640
√2
= 1870 «V»
ALTERNATIVE 2
(Primary) Vrms =
220
√2
(Secondary) Vrms =
= 156 «V»
156×1200
100
Vrms = 1870 «V»
Allow ECF from MP1 and MP2.
Award [2] max for 12.96 V (reversing N p and Ns).
[3 marks]
Examiners report
[N/A]
15e. Describe the use of transformers in electrical power distribution.
[3 marks]
Markscheme
step-up transformers increase voltage/step-down transformers decrease voltage
(step-up transformers increase voltage) from plants to transmission lines / (step-down
transformers decrease voltage) from transmission lines to final utilizers
this decreases current (in transmission lines)
to minimize energy/power losses in transmission
[3 marks]
Examiners report
[N/A]
A negatively charged thundercloud above the Earth’s surface may be modelled by a parallel
plate capacitor.
The lower plate of the capacitor is the Earth’s surface and the upper plate is the base of the
thundercloud.
The following data are available.
Area of thundercloud base
Charge on thundercloud base
Distance of thundercloud base from Earth's surface
Permittivity of air
= 1.2 × 108 m2
= −25 C
= 1600 m
= 8.8 × 10−12 F m−1
16a. Show that the capacitance of this arrangement is C = 6.6 × 10 –7 F.
Markscheme
C = «ε
A
d
=» 8.8 × 10 –12 ×
«C = 6.60 × 10 –7 F»
[1 mark]
1.2×108
1600
[1 mark]
Examiners report
[N/A]
16b. Calculate in V, the potential difference between the thundercloud and the Earth’s
surface.
[2 marks]
Markscheme
V=«
Q
C
=»
25
6.6×10−7
V = 3.8 × 10 7 «V»
Award [2] for a bald correct answer
[2 marks]
Examiners report
[N/A]
16c. Calculate in J, the energy stored in the system.
[2 marks]
Markscheme
ALTERNATIVE 1
E=«
1
QV =»
2
1
2
× 25 × 3.8 × 107
E = 4.7 × 10 8 «J»
ALTERNATIVE 2
E=«
1
CV2 =»
2
1
2
× 6.60 × 10–7 × (3.8 × 10 7)2
E = 4.7 × 10 8 «J» / 4.8 × 10 8 «J» if rounded value of V used
Award [2] for a bald correct answer
Allow ECF from (b)(i)
[2 marks]
Examiners report
[N/A]
Lightning takes place when the capacitor discharges through the air between the thundercloud
and the Earth’s surface. The time constant of the system is 32 ms. A lightning strike lasts for 18
ms.
16d. Show that about –11 C of charge is delivered to the Earth’s surface.
[3 marks]
Markscheme
18
Q = «Q0 e− τ =» 25 × e− 32
t
Q = 14.2 «C»
charge delivered = Q = 25 – 14.2 = 10.8 «C»
«≈ –11 C»
Final answer must be given to at least 3 significant figures
[3 marks]
Examiners report
[N/A]
16e. Calculate, in A, the average current during the discharge.
Markscheme
I «=
ΔQ
Δt
=
11
»
18×10−3
≈ 610 «A»
Accept an answer in the range 597 − 611 «A»
[1 mark]
Examiners report
[N/A]
State one assumption that needs to be made so that the Earth-thundercloud
[1 mark]
16f. State one assumption that needs to be made so that the Earth-thundercloud
system may be modelled by a parallel plate capacitor.
[1 mark]
Markscheme
the base of the thundercloud must be parallel to the Earth surface
OR
the base of the thundercloud must be flat
OR
the base of the cloud must be very long «compared with the distance from the surface »
[1 mark]
Examiners report
[N/A]
17. The plane of a coil is positioned at right angles to a magnetic field of flux density B. The[1 mark]
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.
BA
t
B.
2BA
t
C.
BAN
t
D.
2BAN
t
Markscheme
D
Examiners report
[N/A]
18. The ratio
number of primary turns
number of secondary turns
for a transformer is 2.5.
[1 mark]
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 %
Markscheme
C
Examiners report
[N/A]
19. An alternating current (ac) generator produces a peak emf E0 and periodic time T. What[1 mark]
are the peak emf and periodic time when the frequency of rotation is doubled?
Markscheme
B
Examiners report
[N/A]
20. Six identical capacitors, each of value C, are connected as shown.
What is the total capacitance?
A.
C
6
B.
2C
3
C.
3C
3
D. 6C
Markscheme
B
Examiners report
[N/A]
A capacitor of capacitance C discharges through a resistor of resistance R. The graph
[1 mark]
21. A capacitor of capacitance C discharges through a resistor of resistance R. The graph [1 mark]
shows the variation with time t of the voltage V across the capacitor.
The capacitor is changed to one of value 2 C and the resistor is changed to one of value
2R. Which graph shows the variation with t of V when the new combination is discharged?
Markscheme
B
Examiners report
[N/A]
There is a proposal to power a space satellite X as it orbits the Earth. In this model, X is
There is a proposal to power a space satellite X as it orbits the Earth. In this model, X is
connected by an electronically-conducting cable to another smaller satellite Y.
22a. Satellite X orbits 6600 km from the centre of the Earth.
Mass of the Earth = 6.0 x
10 24
[2 marks]
kg
Show that the orbital speed of satellite X is about 8 km s –1.
Markscheme
«v = √
GM E
r »
=√
6.67×10−11×6.0×1024
6600×103
7800 «m s –1»
Full substitution required
Must see 2+ significant figures.
Examiners report
[N/A]
Satellite Y orbits closer to the centre of Earth than satellite X. Outline why
22b. the orbital times for X and Y are different.
[1 mark]
Markscheme
Y has smaller orbit/orbital speed is greater so time period is less
Allow answer from appropriate equation
Allow converse argument for X
Examiners report
[N/A]
22c. satellite Y requires a propulsion system.
Markscheme
to stop Y from getting ahead
to remain stationary with respect to X
otherwise will add tension to cable/damage satellite/pull X out of its orbit
Examiners report
[N/A]
The cable between the satellites cuts the magnetic field lines of the Earth at right
[2 marks]
22d. The cable between the satellites cuts the magnetic field lines of the Earth at right
angles.
[3 marks]
Explain why satellite X becomes positively charged.
Markscheme
cable is a conductor and contains electrons
electrons/charges experience a force when moving in a magnetic field
use of a suitable hand rule to show that satellite Y becomes negative «so X becomes
positive»
Alternative 2
cable is a conductor
so current will flow by induction flow when it moves through a B field
use of a suitable hand rule to show current to right so «X becomes positive»
Marks should be awarded from either one alternative or the other.
Do not allow discussion of positive charges moving towards X
Examiners report
[N/A]
Satellite X must release ions into the space between the satellites. Explain why
22e. Satellite X must release ions into the space between the satellites. Explain why
the current in the cable will become zero unless there is a method for transferring
charge from X to Y.
[3 marks]
Markscheme
electrons would build up at satellite Y/positive charge at X
preventing further charge flow
by electrostatic repulsion
unless a complete circuit exists
Examiners report
[N/A]
22f. The magnetic field strength of the Earth is 31 µT at the orbital radius of the
satellites. The cable is 15 km in length. Calculate the emf induced in the cable.
Markscheme
«ε = Blv =» 31 x 10 –6 x 7990 x 15000
3600 «V»
Allow 3700 «V» from v = 8000 m s –1.
[2 marks]
Examiners report
[N/A]
The cable acts as a spring. Satellite Y has a mass m of 3.5 x 10 2 kg. Under certain
circumstances, satellite Y will perform simple harmonic motion (SHM) with a period T of 5.2 s.
22g. Estimate the value of k in the following expression.
[3 marks]
T = 2π√ m
k
Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of
satellite X.
Markscheme
use of k = «
4π2m
T2
=»
4×π2×350
5.22
510
N m–1 or kg s–2
Allow MP1 and MP2 for a bald correct answer
Allow 500
Allow N/m etc.
Examiners report
[N/A]
Describe the energy changes in the satellite Y-cable system during one cycle of the
22h. Describe the energy changes in the satellite Y-cable system during one cycle of the
oscillation.
[2 marks]
Markscheme
Ep in the cable/system transfers to Ek of Y
and back again twice in each cycle
Exclusive use of gravitational potential energy negates MP1
Examiners report
[N/A]
23. 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.
5
A
2
C.
5
A
√2
D. 5√2 A
Markscheme
D
Examiners report
[N/A]
What are the units of magnetic flux and magnetic field strength?
[1 mark]
24. What are the units of magnetic flux and magnetic field strength?
[1 mark]
Markscheme
B
Examiners report
[N/A]
25. A battery is used to charge a capacitor fully through a resistor of resistance R. The
energy supplied by the battery is Eb. The energy stored by the capacitor is Ec.
[1 mark]
What is the relationship between Eb and Ec?
A. Eb < Ec
B. Eb = Ec
C. Eb > Ec
D. The relationship depends on R.
Markscheme
C
Examiners report
[N/A]
26. A capacitor is charged by a constant current of 2.5 µA for 100 s. As a result the
potential difference across the capacitor increases by 5.0 V.
What is the capacitance of the capacitor?
A. 20 µF
B. 50 µF
C. 20 mF
D. 50 mF
[1 mark]
Markscheme
B
Examiners report
[N/A]
27. A conducting square coil is placed in a region where there is a uniform magnetic
field. The magnetic field is directed into the page. There is a clockwise current in the
coil.
What is a correct force that acts on a side of the coil?
Markscheme
D
Examiners report
[N/A]
The diagram shows a bar magnet near an aluminium ring.
[1 mark]
28. The diagram shows a bar magnet near an aluminium ring.
[1 mark]
The ring is supported so that it is free to move. The ring is initially at rest. In experiment 1
the magnet is moved towards the ring. In experiment 2 the magnet is moved away from the
ring. For each experiment what is the initial direction of motion of the ring?
Markscheme
B
Examiners report
[N/A]
Three conducting loops, X, Y and Z, are moving with the same speed from a region
29. 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.
[1 mark]
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
Markscheme
A
Examiners report
[N/A]
30. Two capacitors of different capacitance are connected in series to a source of emf of
negligible internal resistance.
[1 mark]
What is correct about the potential difference across each capacitor and the charge on each
capacitor?
Markscheme
C
Examiners report
[N/A]
31. A fully charged capacitor is connected to a resistor. When the switch is closed the
capacitor will discharge through the resistor.
[1 mark]
Which graphs correctly show how the charge on the capacitor and the current in the circuit vary
with time during the discharging of the capacitor?
Markscheme
A
Examiners report
[N/A]
32a. State Faraday’s law of induction.
[2 marks]
Markscheme
the size of the induced emf
is proportional/equal to the rate of change of flux linkage
The word ‘induced’ is required here.
Allow correctly defined symbols from a correct equation. ‘Induced’ is required for MP1.
Examiners report
[N/A]
The diagram shows a sketch of an ideal step-down transformer.
The diagram shows a sketch of an ideal step-down transformer.
The number of turns in the primary coil is 1800 and that in the secondary coil is 90.
32b. Explain, using Faraday’s law of induction, how the transformer steps down the
voltage.
[4 marks]
Markscheme
varying voltage/current in primary coil produces a varying magnetic field
this produces a change in flux linkage / change in magnetic field in the secondary coil
a «varying» emf is induced/produced/generated in the secondary coil
voltage is stepped down as there are more turns on the primary than the secondary
Comparison of number of turns is required for MP4.
Examiners report
[N/A]
The input voltage is 240 V. Calculate the output voltage.
32c. The input voltage is 240 V. Calculate the output voltage.
[2 marks]
Markscheme
output voltage =
90×240
1800
= 12 «V»
Examiners report
[N/A]
32d. Outline how energy losses are reduced in the core of a practical transformer.
Markscheme
laminated core reduces eddy currents
less thermal energy is transferred to the surroundings
Examiners report
[N/A]
Step-up transformers are used in power stations to increase the voltage at which the
[2 marks]
32e. Step-up transformers are used in power stations to increase the voltage at which the [2 marks]
electricity is transmitted. Explain why this is done.
Markscheme
for a certain power to be transmitted, large V means low I
less thermal energy loss as P = I 2R / joule heating
Examiners report
[N/A]
The electrical circuit shown is used to investigate the temperature change in a wire that is
wrapped around a mercury-in-glass thermometer.
A power supply of emf (electromotive force) 24 V and of negligible internal resistance is
connected to a capacitor and to a coil of resistance wire using an arrangement of two switches.
Switch S1 is closed and, a few seconds later, opened. Then switch S 2 is closed.
33a. The capacitance of the capacitor is 22 mF. Calculate the energy stored in the
capacitor when it is fully charged.
[1 mark]
Markscheme
« 12 CV 2 =
1
2
× 0.22 × 242 » = «J»
Examiners report
[N/A]
33b. 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.
Markscheme
1
100
t
= e− 8.0×0.022
ln 0.01 = − 8.0×t0.022
0.81 «s»
Examiners report
[N/A]
The mass of the resistance wire is 0.61 g and its observed temperature rise is 28 K.
[3 marks]
33c. The mass of the resistance wire is 0.61 g and its observed temperature rise is 28 K.
Estimate the specific heat capacity of the wire. Include an appropriate unit for your
answer.
[2 marks]
Markscheme
c=
Q
m×ΔT
OR
6.3
0.00061×28
370 J kg–1 K–1
Allow ECF from 3(a) for energy transferred.
Correct answer only to include correct unit that matches answer power of ten.
Allow use of g and kJ in unit but must match numerical answer, eg: 0.37 J kg
[1]
–1
K–1 receives
Examiners report
[N/A]
33d. Suggest one other energy loss in the experiment and the effect it will have on
the value for the specific heat capacity of the wire.
[2 marks]
Markscheme
ALTERNATIVE 1
some thermal energy will be transferred to surroundings/along connecting wires/to
thermometer
estimate «of specific heat capacity by student» will be larger «than accepted value»
ALTERNATIVE 2
not all energy transferred as capacitor did not fully discharge
so estimate «of specific heat capacity by student» will be larger «than accepted value»
Examiners report
[N/A]
A cable consisting of many copper wires is used to transfer electrical energy from an alternating
A cable consisting of many copper wires is used to transfer electrical energy from an alternating
current (ac) generator to an electrical load. The copper wires are protected by an insulator.
The cable consists of 32 copper wires each of length 35 km. Each wire has a resistance of 64
Ω. The cable is connected to the ac generator which has an output power of 110 MW when the
peak potential difference is 150 kV. The resistivity of copper is 1.7 x 10–8 Ω m.
output power = 110 MW
34a. Calculate the radius of each wire.
Markscheme
area =
1.7×10−3×35×103
64
radius = «√ 9.3×π10
−6
«= 9.3 x 10 –6 m 2»
=» 0.00172 m
Examiners report
[N/A]
[2 marks]
34b. Calculate the peak current in the cable.
[1 mark]
Markscheme
Ipeak «=
Ppeak
»
Vpeak
= 730 « A »
Examiners report
[N/A]
34c. Determine the power dissipated in the cable per unit length.
[3 marks]
Markscheme
resistance of cable identified as «
a power
35000
64
32
=» 2 Ω
seen in solution
2
2I
plausible answer calculated using 35000
«plausible if in range 10 W m –1 to 150 W m –1 when
quoted answers in (b)(ii) used» 31 «W m–1»
Allow [3] for a solution where the resistance per unit metre is calculated using resistivity
and answer to (a) (resistance per unit length of cable = 5.7 x 10–5 m )
Award [2 max] if 64 Ω used for resistance (answer x32).
An approach from
V2
or VI using 150 kV is incorrect (award [0]), however allow this approach if the pd across
R
the cable has been calculated (pd dropped across cable is 1.47 kV).
Examiners report
[N/A]
To ensure that the power supply cannot be interrupted, two identical cables are connected in
parallel.
34d. Calculate the root mean square (rms) current in each cable.
[1 mark]
Markscheme
«
response to (b)(ii)
2√2
» = 260 «A»
Examiners report
[N/A]
34e. The two cables in part (c) are suspended a constant distance apart. Explain how
[2 marks]
the magnetic forces acting between the cables vary during the course of one cycle of
the alternating current (ac).
Markscheme
wires/cable attract whenever current is in same direction
charge flow/current direction in both wires is always same «but reverses every half cycle»
force varies from 0 to maximum
force is a maximum twice in each cycle
Award [1 max] if response suggests that there is repulsion between cables at any stage in
cycle.
Examiners report
[N/A]
The energy output of the ac generator is at a much lower voltage than the 150 kV used for
transmission. A step-up transformer is used between the generator and the cables.
34f. Suggest the advantage of using a step-up transformer in this way.
Markscheme
higher voltage gives lower current
«energy losses depend on current» hence thermal/heating/power losses reduced
Examiners report
[N/A]
The use of alternating current (ac) in a transformer gives rise to energy losses. State
[2 marks]
34g. The use of alternating current (ac) in a transformer gives rise to energy losses. State
how eddy current loss is minimized in the transformer.
[1 mark]
Markscheme
laminated core
Do not allow “wires are laminated”.
Examiners report
[N/A]
35. Which of the following reduces the energy losses in a transformer?
A. Using thinner wires for the windings.
B. Using a solid core instead of a laminated core.
C. Using a core made of steel instead of iron.
D. Linking more flux from the primary to the secondary core.
Markscheme
D
Examiners report
[N/A]
The secondary coil of an alternating current (ac) transformer is connected to two diodes
[1 mark]
36. The secondary coil of an alternating current (ac) transformer is connected to two diodes [1 mark]
as shown.
Which graph shows the variation with time of the potential difference VXY between X and Y?
Markscheme
A
Examiners report
[N/A]
37. A parallel-plate capacitor is connected to a battery. What happens when a sheet of
dielectric material is inserted between the plates without disconnecting the battery?
A. The capacitance is unchanged.
B. The charge stored decreases.
C. The energy stored increases.
D. The potential difference between the plates decreases.
Markscheme
C
[1 mark]
Examiners report
[N/A]
38. Three capacitors are arranged as shown.
[1 mark]
What is the total capacitance of the arrangement?
A. 1.0F
B. 2.5F
C. 3.0F
D. 4.0F
Markscheme
A
Examiners report
[N/A]
The following data are available for a natural gas power station that has a high efficiency.
The following data are available for a natural gas power station that has a high efficiency.
Rate of consumption of natural gas
Specific energy of natural gas
Efficiency of electrical power
generation
Mass of CO 2 generated per kg of
natural gas
One year
= 14.6 kg s –1
= 55.5 MJ kg –
1
= 59.0 %
= 2.75 kg
= 3.16 × 10 7 s
39a. Electrical power output is produced by several alternating current (ac) generators
which use transformers to deliver energy to the national electricity grid.
[4 marks]
The following data are available. Root mean square (rms) values are given.
ac generator output voltage to a transformer = 25 kV ac generator output current to a
transformer = 3.9 kA Transformer output voltage to the grid = 330 kV Transformer efficiency =
96%
(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.
Markscheme
i
I = 0.96 × ( 25×10 ×3.93×10 )
3
3
330×10
Award [2] for a bald correct answer to 2 sf.
Award [1 max] for correct sf if efficiency used in denominator leading to 310 A or if
efficiency ignored (e=1) leading to 300 A (from 295 A but 295 would lose both marks).
=280 «A»
Must show two significant figures to gain MP2.
ii
higher V means lower I «for same power»
thermal energy loss depends on I or is ∝I2 or is I2R so thermal energy loss will be less
Accept “heat” or “heat energy” or “Joule heating” for “thermal energy”.
Reference to energy/power dissipation is not enough.
Examiners report
[N/A]
39b. In an alternating current (ac) generator, a square coil ABCD rotates in a magnetic
field.
[5 marks]
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.
Dimensions of the coil = 8.5 cm×8.5 cm Number of turns on the coil = 80 Speed of edge AB =
2.0 ms–1 Uniform magnetic field strength = 0.34 T
(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.
Markscheme
i
«long» sides of coil AB/CD cut lines of flux
OR
flux «linkage» in coil is changed
«Faradays law:» induced emf depends on rate of change of flux linked
OR
rate at which lines are cut
“Induced” is required
Allow OWTTE or defined symbols if “induced emf” is given.
Accept “induced” if mentioned at any stage in the context of emf or accept the term
“motional emf”.
Award [2 max] if there is no mention of “induced emf”.
emfs acting in sides AB/CD add / act in same direction around coil
process produces an alternating/sinusoidal emf
ii
Blv = 0.34×8.5×10 –2×2 = 0.058 «V»
Accept 0.06V.
iii
160×(c)(ii) = 9.2 or 9.3 or 9.6 «V»
Allow ECF from (c)(ii)
If 80 turns used in cii, give full credit for cii x 2 here.
Examiners report
[N/A]
A coil of area A is placed in a region of uniform horizontal magnetic field B. At t=0, the
40. A coil of area A is placed in a region of uniform horizontal magnetic field B. At t=0, the [1 mark]
coil starts to rotate with constant angular speed ω about a horizontal axis.
What is the emf between X and Y?
A. zero
B. ωAB sin ωt
C. AB cos ωt
D. −ωAB sin ωt
Markscheme
A
Examiners report
[N/A]
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