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1
Guide to STPM Practicals
Guidelines for STPM Physics Practical Examination
Introduction
This practical guide lists the aims, apparatus and procedures for selected experiments. The techniques, precautions, formulae and calculations which are relevant to the experiments are also included.
The section on techniques brings attention to more efficient means of conducting the experiments. The section on precautions lists the steps to ensure a smaller error margin in the results obtained. The section on formulae and calculations helps students apply the results of the experiments and obtain the final conclusion.
This practical guide does not provide experimental data or results. The actual data and results are subject to the specific conditions under which the experiments were conducted.
2
SAMPLE EXPERIMENT
Aim: To measure the resistance of a nichrome wire.Apparatus: 1. SWG 32 nichrome wire (1m in length) 2. D.C. power supply 3. Rheostat 4. Digital ammeter 5. Digital voltmeter 6. SwitchProcedure: 1. Set up the circuit as shown below.
2. Do a rough check to estimate the suitable range of voltage readings and ammeter readings. 3. Close the switch and adjust the rheostat so that a small current passes through the nichrome
wire. 4. Record the ammeter readings I and voltage readings V. Switch off the current when the measurements
have been recorded. 5. Let the wire cool down. 6. Repeat steps 3 and 4 for different values of I. 7. Plot a graph of I against V. 8. Use the graph to calculate the value of the resistance R of the nichrome wire.
Results:
Current, I (A) Voltage, V (V)
0.01 0.18
0.02 0.36
0.03
0.04
0.05
0.06
0.07
Uncertainties in the readings of digital ammeter and digital voltmeter are ±0.01A and ±0.01V respectively. Hence, the readings are recorded to two decimal places
The number of decimal places for all data must be consistent
Responding variables are on the right-hand side
The quantity and unit of measurement for each column must be shown, for example, I (A) and V (V)
Manipulated variables are on the left-hand side
SWG 32 nichromewire (1m in length)
Rheostat
A
V
3
Graph of I against V
Calculations: V R = — I 1 I — = — = gradient R V 1 R = ———— gradient
y2 – y1From the graph, gradient = ———— = b x2 – x1
1 ∴ R = — = k Ω b
Sources of error: 1. The nichrome wire overheats. 2. Zero errors of digital ammeter and voltmeter. 3. Short-circuit occurs. 4. The digital ammeters or voltmeters are overloaded.
Steps taken to reduce the errors/overcome the limitations: 1. Let the wire cool down before making the next measurement. 2. Correct the zero error if it exists. 3. Check all the connections to make sure that there are no loose connections and the connecting
wires are not exposed. 4. Do a rough check to estimate the suitable range of ammeter and voltmeter readings before starting
the experiment. It is advisable to use a large number of separate readings than to take repeated readings since it is difficult to reset the current to its previous value due to overheating.
Quantity (unit)
I (A)
V (V)0
(x1, y1)
(x2, y2) For a straight line graph, draw the line of best fit by ensuring that the points scatter equally about the line
Good choices of scales are 1: 1, 1: 5, 1: 10, and so on
Quantity (unit)
4
Chapter 2 Capacitors
Experiment AAim: To determine the time constant and the capacitance of capacitors in an RC circuit.Procedure: 1. Set up the circuit shown below.
2. Connect the points X and Y using crocodile clips to a resistor-pack for different values of effective resistance R.
3. Starting with R = 6600 Ω, close switch S and decrease R in stages until the milliammeter reading I0 is approximately 1.0 mA.
Precautions:• Before using the milliammeter, check whether it has a zero error. If there is a zero error, calibrate
the milliammeter.• All components of the circuit must be properly connected.
4. Record the value of I0 and the corresponding resistance R0. 5. Open switch S and connect a short wire across the terminals of the capacitor to fully discharge
it.
Technique: • The capacitor is fully discharged when the reading of the milliammeter is 0 A.
6. Close switch S again to charge the capacitor until the milliammeter shows I0. 7. Simultaneously open switch S and start the stopwatch. When the current I reaches a certain value,
stop the stopwatch. 8. Repeat steps 6 and 7 to obtain values of I and t.
I0 I0 9. Record and tabulate I, t, — and ln —. t I10. Add another capacitor C2 as shown below. The value of R is fixed at R0.
11. Repeat steps 5, 6, 7, 8 and 9 to obtain the milliammeter reading I' and the corresponding time t'.
I0 I012. Plot a graph of ln — against t and a graph of ln — against t' on the same axis. I I'
Switch S
6 V d.c. supply+
−
X
Y
Connectedto resistor-pack
mA
CapacitorC1
Switch S
6 V d.c. supply+
−
CapacitorC1
CapacitorC2
X
Y
Connectedto resistor-pack
mA
Milliammeter
5
Formula: t – —– I = I0e CR
where I0 = initial current I = current at time t seconds C = capacitance R = resistance
Calculations: t – —–
I = I0e CR
t I0 —–
—– = e CR
I
I0 t ln —– = —– I CR
I0 1 ln —– = —–t I CR
I0 ∆ ln —– I Gradient, k = ————– ∆ t 1 = —– CR
1 Capacitance, C = —– kR 1 Time constant, τ = — = CR k
Chapter 3 Electric Current
Experiment BAim: To verify Ohm’s law and to find the total resistance of resistors connected in series and in
parallel.Procedure: 1. Set up the circuit shown below.
2. Close the switch S and adjust the rheostat so that the ammeter shows a reading of I = 1.00 A. 3. Record the voltmeter reading V. 4. Repeat steps 2 and 3 using different values of I = 1.10 A, 1.20 A, 1.30 A, and 1.40 A.
Technique:• Take readings at smaller current intervals so that the graph can be plotted more accurately.
5. Plot a graph of I against V.
y-axis Gradient x-axis
lnI0
I
InI0
I∆
InI0
I'∆
t∆
t'∆
t (s)0
Rheostat
A
V
Switch S4.5 V
6
6. Set up another circuit as shown below.
7. Repeat steps 2, 3, 4 and 5.
Formula: V R = — (Ohm’s law) I where R = total resistance V = potential difference I = current
Calculations:Both the graphs of I against V for resistors in series and in parallel pass through the origin, that is, I is directly proportional to V. Hence, Ohm’s law is verified.
∆ I Gradient, k = —– ∆V
1 Total resistance, R = —– k
Chapter 4 Direct Current Circuits
Experiment CAim: To find the resistivity of the material of a wire using a Wheatstone bridge.Procedure: 1. Set up the circuit shown below.
2. Use an approximately 50 cm long SWG 36 constantan wire as resistor X.
Precautions:• Make sure the wires do not cross each other.
3. Place a standard resistor P in the right-hand gap. 4. Turn on the switch S and slide the jockey gently along the slide wire AB until the centre-zero
galvanometer is balanced.
Rheostat
A
V
0
I (A)
V (V)
I∆
V∆
Parallel
Series
Switch S
a1 b1
C
X
A
D
B
P
JockeyG
7
Technique:• Slide the jockey slowly along the slide wire AB.• Press the jockey lightly on the slide wire AB so as not to change the diameter of the wire.
5. Record the values of P, a1 and b1. 6. Reverse the terminals of the cells and repeat step 4. 7. Record the values of a2 and b2. 8. Interchange X and P and repeat step 4. 9. Record the values of a3 and b3.10. Reverse the terminals of the cells and repeat step 4.11. Record the values of a4 and b4.12. Calculate l1 where l1 is the mean of a1, a2, b3 and b4. Calculate l2 where l2 is the mean of b1, b2, a3 and a4.13. Measure the length x of wire X in the left-hand gap followed by its diameter d.14. Calculate the resistance of X and its resistivity.
Precautions:• The experiment should be repeated by placing the unknown resistor X in the right-hand gap and
the standard resistor P in the left-hand gap to eliminate end errors.• The standard resistor P should be chosen carefully so that the centre-zero galvanometer is balanced
within the range from 30 cm to 70 cm on the slide wire AB.
Formula: 1. Resistance R of a wire of length l and cross-sectional area A is given by
ρl R = —– A
where ρ = resistivity of the wire 2. When a Wheatstone bridge is balanced,
r1 l1 —– = —– r2 l2
where r1 and r2 = resistances connected across the gaps l1 and l2 = lengths of the slide wire on both sides of the balance point
Calculations:When the centre-zero galvanometer is balanced,
X l1 — = — P l2
l1 X = —P l2
ρl Using R = —–, A
d Xπ—2 RA 2 ρ = —– = ————– l x
πd2X Resistivity, ρ = ——– 4x
8
Chapter 4 Direct Current Circuits
Experiment DAim: To calculate the internal resistance of a cell using a potentiometer.Procedure: 1. Set up the circuit shown below.
2. Close switch S and open switch S'. 3. Slide the jockey gently along the slide wire until the centre-zero galvanometer is balanced.
Technique:• Another method to avoid pressing too hard on the slide wire is to touch the slide wire with the
jockey at various points along the wire until the balance point is determined.
4. Record the balanced length l0. 5. Close both switches S and S'. 6. Repeat step 3. 7. Record the balanced length l for different values of R.
l0 8. Tabulate the results of l, —– and R. l
l0 1 9. Plot a graph of —– against —–. l R10. Calculate the internal resistance r of the cell.
Formula: ε = V + Ir where ε = e.m.f. of dry cell V = potential difference across external circuit I = current r = internal resistance Using ε = V + Ir,
ε – V r = ——— I
ε – V = ——— V — R
ε = R— – 1 V
l0 ε l0 = R—– – 1 From potentiometer, — = —– l V l
l0 1 —– = r— + 1 l R
Switch S
Switch S'
G
P Q
Resistor R
l0
l0l
l0l
01r−
1R
1R
∆
∆
9
Chapter 5 Magnetic Fields
Experiment EAim: To investigate the behaviour of a bar magnet in varying magnetic fields of a solenoid and hence
calculate the horizontal component of the Earth’s magnetic field.Procedure: 1. Set up the apparatus as shown below.
2. Hang a bar magnet as shown above so that it stays 5 cm above the table.
Precautions:• All magnetic materials including the ammeter must be placed far away from the bar magnet.
3. Make sure the magnet is stationary. 4. Place a mirror with a paper protractor below the bar magnet. The 0° – 180° axis of the mirror is
placed parallel to the bar magnet. 5. Place the solenoid horizontally at the same height as the bar magnet. The axis of the solenoid must
be perpendicular to the axis of the magnet. 6. The end of the solenoid is 3.0 cm from the axis of the magnet. 7. Connect the solenoid to the electric circuit shown above.
Technique:• The whole apparatus must be placed on a flat surface.• The apparatus must be shielded from wind to keep the bar magnet stationary.
Precautions:• The ammeter must be placed far from the magnet so that the magnetic field induced by the ammeter
does not interfere with the magnet.
8. Adjust the rheostat to its maximum resistance and turn on the switch. 9. Record the ammeter reading I and the average deflection θ of the magnet from the 0° – 180°
axis.10. Repeat step 9 using smaller values of resistances.11. Tabulate the readings of I, θ and tan θ.12. Plot a graph of tan θ against I.13. Find the gradient s of the graph where I = 0.20 A.14. Measure the internal diameter D, average diameter d of the wire and the length L of the
solenoid.
Technique:• Use the proper instruments to measure the required quantities. – Internal diameter D of solenoid: Vernier calliper – Average diameter d of the wire: Micrometer screw gauge – Length L of solenoid: Metre rule
Axis ofbar magnet
Axis ofsolenoid
90o
90o90o
90o
0o
Mirror
Paperprotractor
A
180o
10
15. Calculate the number of turns N using the values of d and L.
Formula:Horizontal component of the Earth’s magnetic field,
µ0N 1 BH ≈ ——–1 – ————– 2Ls D2
l2 + —– 4 where BH = horizontal component of the Earth’s magnetic field µ0 = 4 × 10–7 H m–1
l = 0.030 m
Chapter 8 Electronics
Experiment FAim: To calculate the voltage gain and the bandwidth of an operational amplifier.Part 1: To calculate the gain of an inverting amplifier with a d.c. voltage input.Procedure: 1. Set up the circuit as shown below.
Precautions:• Make sure the connections in the above circuit are not loose.• Test the circuit board to make sure it is not faulty.
2. Turn on switch A and turn off switch B. 3. Adjust the rheostat so that the digital multimeter reading Vi = 0.1 V. Record the value of Vi. 4. Turn off both switches A and B. Record the digital multimeter reading Vo. 5. Repeat steps 2, 3 and 4 with increasing values of Vi until Vi = 1.2 V. 6. Tabulate Vi and Vo. 7. Plot a graph of Vo against Vi.
Formula: Ro Vo = – ——Vi Ri
Vo Ro So, gain, A = —– = —– Vi Ri
where Vo = output voltage Vi = input voltage Ro and Ri = resistances of resistors in the circuit board
Rheostat
Vi
VO
VO3 V
PB
Q
Inverting input
Non-invertinginput
Circuit board
Ground
A
V
11
Calculations:
Ro Vo = –—–Vi Ri
Ro Vo Gradient = – —– = —– = A Ri Vi
∴ A = – (gradient)
Part 2: To calculate the gain and bandwidth of the frequency response of an inverting amplifier with an a.c. voltage input (sinusoidal).
Procedure: 1. Remove both the 3 V dry cell and the rheostat and replace them with a signal generator. 2. Set the digital multimeter to measure an a.c. voltage. The frequency f of the generator is set at
1 kHz.
Precautions:• Always check whether the digital multimeter has a zero error before using it.
3. Turn on switch A and turn off switch B. The input voltage Vi of the generator is adjusted so that the digital multimeter reading is between 0.100 V and 0.150 V. Record both the values of Vi and f.
4. Turn off switch B and turn on switch A. Record the value of the output voltage Vo on the digital multimeter.
5. Repeat steps 2, 3 and 4 using different values of f up to 30 kHz.
Vo 6. Tabulate f, Vi, Vo and A = —–. Vi
7. Plot a graph of A against f.
Formula:
Vi A = —– Vo
Calculations:For bandwidth = f1 Hz, gain = A1
For bandwidth = f2 Hz, gain = A2
For bandwidth = f3 Hz, gain = A3
Chapter 10 Geometrical Optics
Experiment GAim: To calculate the focal length of a convex lens.Procedure: 1. Set up the apparatus as shown below.
y-axis Gradient x-axis
Vo
Vi0
ƒ1
ƒ2
ƒ3
A
A1
ƒ(Hz)
A2
A3
0
12
2. Mark a length of h = 2 cm on the transparent ruler to act as the object. 3. Measure and record the distance u of the transparent ruler from the convex lens. 4. Change the position of the object. Determine v and the size of the image H on the screen.
Technique:• Perform the experiment in a dark room so that the size of the image H can be clearly seen.• Adjust the position of the object until a sharp image is formed on the screen.
v 5. Calculate the linear magnification m = — and tabulate the results for u, v and m. u 6. Plot a graph of m against v.
Formula:
1 1 1 — + — = — u v f
where f = focal length of the convex lens
Calculations:
1 1 1 — + — = — u v f v v — + 1 = — u f v m + 1 = — f 1 m = — v – 1 f
Chapter 10 Geometrical Optics
Experiment HAim: To estimate the refractive index of glass using a concave mirror.Procedure: 1. Measure and record the thickness t of each glass block. 2. Set up the apparatus as shown below.
y-axis Gradient x-axis y-intercept
Transparentruler
Lens
Screen
Plasticine
RulerRay box
u
h
v
v (cm)
m
0
−1
∆v
∆m
1 Gradient = — f
1 f = ———— gradient
13
3. Adjust the position of the bulb until the image coincides with the bulb. Record the height h of the bulb above the table.
Technique:• The eye must be directly above the bulb at all times.
4. Place a glass block on the wooden block as shown below.
5. Repeat step 3. 6. Add one glass block at a time and repeat step 3. 7. Tabulate the number of glass blocks m and the corresponding heights of the bulb h. 8. Plot a graph of h against m.
Formula:
1 h – ho = mt 1 – —– nk
where h = height of the bulb above the table when m glass blocks are placed on the wooden blocks
ho = height of the bulb above the table without the glass blocks t = thickness of each glass block nk = refractive index of glass
Calculations:
1 h – ho = mt 1 – —– nk
1 h = t1 – —–m + ho nk
Retortstand
Powersupply
Bulb
Eye
Image
Concavemirror
Wooden blocks
h
hho
Glassblock
Concave mirror
Wooden blocks
t
t
mt
y-axis Gradient x-axis y-intercept
⎫ ⎪ ⎬ ⎪ ⎭
14
1 Gradient = t 1 – —– nk
1 gradient 1 – —– = ———— nk t
1 gradient —– = 1 – ———— nk t
1 t – gradient —– = —————– nk t
t nk = ————— t – gradient
Chapter 11 Physical Optics
Experiment IAim: To study the diffraction pattern formed by a diffraction grating and to determine the wavelength
of a laser beam.Procedure: 1. Set up the apparatus as shown below.
2. The laser pointer is directed towards the diffraction grating.
Precautions:• The incident ray from the laser pointer must be normal to the diffraction grating.• The screen must be parallel to the plane of the diffraction grating.• Both the diffraction grating and screen must be vertical.
3. Adjust the distance D between the diffraction grating and the screen to give the bright spots the maximum possible separation.
4. Use the diffraction grating with N = (80 to 100) lines/mm to determine l1, l2, l3,… for the 1st, 2nd, 3rd, … order of diffraction.
Technique:• Use a ruler to measure the distance between each bright spot on opposite sides of the 0th order
diffraction. Divide this distance by 2 to obtain the values of l1, l2, l3, …
ho
h (cm)
0 m
∆m
∆h
Laser pointer Diffraction grating
Screen
y1l1 = —– 2
y2l2 = —– 2
2nd order
2nd order
1st order
1st order
0th order y1
y2
15
l 5. Determine the value of sin θn for n = 1, 2, 3, … from the equation sin θn = ———— l2 + D2
6. Plot a graph of sin θn against n, where n = 1, 2, 3, … 7. Replace the original diffraction grating with another diffraction grating with a different value of
N. Repeat steps 1, 2, 3, 4 and 5.
Formula: nλ sin θn = —– D where θn = angle of the nth diffraction D = distance between the diffraction grating and the screen n = order of diffraction λ = wavelength of incident ray
1 N = — d where N = number of lines per mm d = separation of the grating
Calculations:
λ sin θn = —– n d
λ Gradient = —– d λ = (gradient) × d 1 = (gradient) × —– N 1 where N = — d
y-axis Gradient x-axis
0 n
∆ sin θn
Sin θn
∆n