1
(a)
(i)
Describe how you would make a direct measurement of the emf ɛ of a cell, stating
the type of meter you would use.
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(1)
(ii)
Explain why this meter must have a very high resistance.
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(1)
(b)
A student is provided with the circuit shown in the diagram below.
The student wishes to determine the efficiency of this circuit.
In this circuit, useful power is dissipated in the external resistor. The total power input is the
power produced by the battery.
Efficiency =
The efficiency can be determined using two readings from a voltmeter.
(i)
Show that the efficiency =
where ɛ is the emf of the cell
and V is the potential difference across the external resistor.
(1)
Page 1 of 18
(ii)
Add a voltmeter to the diagram and explain how you would use this new circuit to
take readings of ɛ and V.
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(2)
(c)
Describe how you would obtain a set of readings to investigate the relationship between
efficiency and the resistance of the external resistor. State any precautions you would take
to ensure your readings were reliable.
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(2)
(d)
State and explain how you would expect the efficiency to vary as the value of R is
increased.
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(2)
(Total 9 marks)
Page 2 of 18
2
A student has a diffraction grating that is marked 3.5 × 103 lines per m.
(a)
Calculate the percentage uncertainty in the number of lines per metre suggested by this
marking.
percentage uncertainty = ..................................... %
(1)
(b)
Determine the grating spacing.
grating spacing = ..................................... mm
(2)
(c)
State the absolute uncertainty in the value of the spacing.
absolute uncertainty = ..................................... mm
(1)
Page 3 of 18
(d)
The student sets up the apparatus shown in Figure 1 in an experiment to confirm the value
marked on the diffraction grating.
Figure 1
The laser has a wavelength of 628 nm. Figure 2 shows part of the interference pattern that
appears on the screen. A ruler gives the scale.
Figure 2
Use Figure 2 to determine the spacing between two adjacent maxima in the
interference pattern. Show all your working clearly.
spacing = ..................................... mm
(1)
(e)
Calculate the number of lines per metre on the grating.
number of lines = .....................................
(2)
Page 4 of 18
(f)
State and explain whether the value for the number of lines per m obtained in part (e) is in
agreement with the value stated on the grating.
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(2)
(g) State one safety precaution that you would take if you were to carry out the experiment that
was performed by the student.
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(1)
(Total 10 marks)
Page 5 of 18
3
Data analysis question
Capillary action can cause a liquid to rise up a hollow tube. Figure 1 shows water that has risen
to a height h in a narrow glass tube because of capillary action.
Figure 1
Figure 2 shows the variation of h with temperature θ for this particular tube.
Figure 2
θ / °C
The uncertainty in the measurement of h is shown by the error bars. Uncertainties in the
measurements of temperature are negligible.
Page 6 of 18
(a)
Draw a best-fit straight line for these data (Figure 2).
(1)
(b)
It is suggested that the relationship between h and θ is
h = h0 — h( 0k)θ
where h0 and k are constants.
Determine h0.
h0 = = ..................................... mm
(1)
(c)
Show that the value of h0k is about 0.9 mm K–1.
(3)
(d)
Determine k. State a unit for your answer.
k = ............................... unit = ...............................
(2)
Page 7 of 18
(e)
A similar experiment is carried out at constant temperature with tubes of varying internal
diameter d. Figure 3 shows the variation of h with
at a constant temperature.
Figure 3
d–1 / mm–1
It is suggested that capillary action moves water from the roots of a tree to its leaves.
The gradient of Figure 3 is 14.5 mm2.
The distance from the roots to the top leaves of the tree is 8.0 m.
Calculate the internal diameter of the tubes required to move water from the roots to the
top leaves by capillary action.
(2)
(f)
Comment on the accuracy of your answer for the internal tube diameter in part (v).
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(1)
(Total 10 marks)
Page 8 of 18
4
This question is about capacitor charging and discharging.
A student designs an experiment to charge a capacitor using a constant current. The figure
below shows the circuit the student designed to allow charge to flow onto a capacitor that has
been initially discharged.
The student begins the experiment with the shorting lead connected across the capacitor as in
the figure above. The variable resistor is then adjusted to give a suitable ammeter reading. The
shorting lead is removed so that the capacitor begins to charge. At the same instant, the stop
clock is started.
The student intends to measure the potential difference (pd) across the capacitor at 10 s intervals
while adjusting the variable resistor to keep the charging current constant.
The power supply has an emf of 6.0 V and negligible internal resistance. The capacitor has a
capacitance of 680 µF. The variable resistor has a maximum resistance of 100 kΩ.
(a)
The student chooses a digital voltmeter for the experiment. A digital voltmeter has a very
high resistance.
Explain why it is important to use a voltmeter with very high resistance.
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(1)
(b)
Suggest one advantage of using an analogue ammeter rather than a digital ammeter for
this experiment.
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(1)
Page 9 of 18
(c)
Suggest a suitable full scale deflection for an analogue ammeter to be used in the
experiment.
full scale deflection = ............
(2)
(d)
The diagram shows the reading on the voltmeter at one instant during the experiment. The
manufacturer gives the uncertainty in the meter reading as 2%.
Calculate the absolute uncertainty in this reading.
uncertainty = ............V
(1)
(e)
Determine the number of different readings the student will be able to take before the
capacitor becomes fully charged.
number = ............
(3)
Page 10 of 18
(f)
The experiment is performed with a capacitor of nominal value 680 µF and a manufacturing
tolerance of ± 5 %. In this experiment the charging current is maintained at 65 µA. The data
from the experiment produces a straight-line graph for the variation of pd with time. This
shows that the pd across the capacitor increases at a rate of 98 mV s–1.
Calculate the capacitance of the capacitor.
capacitance = ............µF
(2)
(g)
Deduce whether the capacitor is within the manufacturer’s tolerance.
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(1)
(h)
The student decides to confirm the value of the capacitance by first determining the time
constant of the circuit when the capacitor discharges through a fixed resistor.
Describe an experiment to do this. Include in your answer:
•
•
•
a circuit diagram
an outline of a procedure
an explanation of how you would use the data to determine the time constant.
Page 11 of 18
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(4)
(Total 15 marks)
Page 12 of 18
Mark schemes
1
(a)
(i)
Voltmeter across terminals with nothing else connected to battery / no additional load.
✓
1
(ii)
This will give zero / virtually no current ✓
1
(b)
(i)
Answer must clearly show power: εI and VI, with I cancelling out to give
formula stated in the question ✓
1
(ii)
Voltmeter connected across cell terminals ✓
Switch open, voltmeter records ε
Switch closed, voltmeter records V
Both statements required for mark ✓
Candidates who put the voltmeter in the wrong place can still
achieve the second mark providing they give a detailed description
which makes it clear that:
To measure emf, the voltmeter should be placed across the cell with
the external resistor disconnected
And
To measure V, the voltmeter should be connected across the
external resistor when a current is being supplied by the cell
2
(c)
Vary external resistor and measure new value of V, for at least 7 different values of
external resistor ✓
Precautions - switch off between readings / take repeat readings (to check that emf or
internal resistance not changed significantly) ✓
2
(d)
Efficiency increases as external resistance increases ✓
Explanation
Efficiency = Power in R / total power generated
I2R / I2(R + r) = R / (R + r)
So as R increases the ratio becomes larger or ratio of power in load to power in
internal resistance increases ✓
Explanation in terms of V and ε is acceptable
2
[9]
2
(a)
2.9% ✓
Allow 3%
1
Page 13 of 18
(b)
seen ✓
1
0.29 mm or 2.9 x 10-4 m✓ must see 2 sf only
1
(c)
± 0.01 mm ✓
1
(d)
Clear indication that at least 10 spaces have been measured to give a spacing = 5.24
mm✓
spacing from at least 10 spaces
Allow answer within range ±0.05
1
(e)
Substitution in d sinθ = nλ✓
The 25 spaces could appear here as n with sin θ as 0.135 / 2.5
1
d = 0.300 x 10-3 m so
number of lines = 3.34 x103✓
Condone error in powers of 10 in substitution
Allow ecf from 1-4 value of spacing
1
(f)
Calculates % difference (4.6%) ✓
1
and makes judgement concerning agreement ✓
Allow ecf from 1-5 value
1
(g)
care not to look directly into the laser beam✓
OR
care to avoid possibility of reflected laser beam ✓
OR
warning signs that laser is in use outside the laboratory✓
ANY ONE
1
[10]
Page 14 of 18
3
(a)
Straight line of best fit passing through all error bars ✓
Look for reasonable distribution of points on either side
1
(b)
h0 = 165 ± 2 mm✓
1
(c)
Clear attempt to determine gradient ✓
1
Correct readoffs (within ½ square) for points on line more than 6 cm apart and
correct substitution into gradient equation ✓
1
h0k gradient =( -) 0.862 mm K-1 and
negative sign quoted ✓
Condone negative sign
Accept range -0.95 to -0.85
1
(d)
k=
= 5.2 x 10-3 ✓
Allow ecf from candidate values
1
K-1 ✓
Accept range 0.0055 to 0.0049
1
(e)
for h = 8000 mm, d-1 =
✓
1
d = 1.8 x 10-3 mm ✓
1
Page 15 of 18
(f)
Little confidence in this answer because
One of
It is too far to take extrapolation ✓
OR
This is a very small diameter ✓
1
[10]
4
(a)
Capacitor must not lose charge through the meter ✓
1
(b)
Position on scale can be marked / easier to read quickly etc ✓
1
(c)
Initial current =
= 60.0 μA ✓
100 μA or 200 μA ✓ (250 probably gives too low a reading)
Give max 1 mark if 65 μA (from 2.6) used and 100 μA meter chosen
2
(d)
0.05 V ✓
1
(e)
Total charge = 6.0 x 680 x 10-6 (C) (= 4.08 mC) ✓
Time = 4.08 x 10-3 / 60.0 x 10-6 = 68 s ✓
Hence 6 readings ✓
3
(f)
Recognition that total charge = 65 t μC and final pd = 0.098 t
so C = 65μ / 0.098✓
660 μF ✓
Allow 663 μF
2
(g)
(yes) because it could lie within 646 – 714 to be in tolerance ✓
OR
it is 97.5 % of quoted value which is within 5% ✓
1
Page 16 of 18
(h)
Suitable circuit drawn ✓
Charge C then discharge through R and record V or I at 5 or 10 s intervals ✓
Plot ln V or ln I versus time ✓
gradient is 1 / RC ✓
OR
Suitable circuit drawn ✓
Charge C then discharge through R and record V or I at 5 or 10 s intervals✓
Use V or I versus time data to deduce half-time to discharge ✓
1 / RC = ln 2 / t½ quoted ✓
OR
Suitable circuit drawn ✓
Charge C then discharge through R and record V or I at 5 or 10 s intervals ✓
Plot V or I against t and find time T for V or I to fall to 0.37 of initial value ✓
T = CR ✓
Either A or V required
For 2nd mark, credit use of datalogger for recording V or I.
4
[15]
Page 17 of 18
Examiner reports
1
(a)
(b)
(i)
Students had to make it clear that the voltmeter ‘alone’ should be connected across
the cell.
(ii)
A correct explanation was given by a large proportion of students.
(i)
Answered well by the more able students.
(ii)
A proportion of students seemed to understand how to use the voltmeter but failed to
show the correct position on the circuit diagram.
(c)
This question discriminated well. Many students failed to give sufficient detail as required
by the mark scheme for the first marking point. The second marking point proved to be
more accessible, with a greater proportion of students able to suggest an appropriate
precaution.
(d)
As anticipated this proved to be very demanding, with only the more able students
successfully stating and explaining why efficiency would increase as external resistance
increases.
Page 18 of 18