Required practical activities 1-6

Q: What is the difference between accuracy and precision in physics measurements?

Accuracy describes how close a measured value is to the true value , whereas precision describes the closeness of agreement among repeated independent measurements (reflecting only random error spread).

Q: How do random and systematic errors differ in their causes and remediation?

Random errors cause unpredictable scatter around the true value and are reduced by repeating readings and taking a mean. Systematic errors shift readings by a constant amount and cannot be reduced by repeats; they require recalibration, zero-offset correction, or improved technique.

Q: What are the algebraic rules for combining uncertainties when adding, multiplying, and raising to powers?

For addition/subtraction ( \(y = a \pm b\)), add absolute uncertainties : \(\Delta y = \Delta a + \Delta b\). For multiplication/division (\(y = ab\) or \(y = a/b\)), add percentage uncertainties : \(\%\Delta y = \%\Delta a + \%\Delta b\). For powers (\(y = a^n\)), multiply percentage uncertainty by \(|n|\): \(\%\Delta y = |n| \times \%\Delta a\).

Q: In Required Practical 2, how do you determine the wavelength of light using double slits and a diffraction grating?

For double slits : measure fringe spacing \(w\) over multiple fringes and use \(w = \frac{\lambda D}{s}\) (gradient of \(w\) vs \(D\) is \(\frac{\lambda}{s}\)). For a diffraction grating : use \(d\sin\theta = n\lambda\) (gradient of \(\sin\theta\) vs \(n\) is \(\frac{\lambda}{d}\)).

Physics 7407 · AQA AS Level · 15 min read · Updated: 7 Sept 2026

Welcome to AS Level Practical Physics

Welcome to your complete study guide for Practical Skills and Required Practicals 1 to 6 in AQA AS Level Physics (7407). Practical skills are not just about laboratory work; they make up at least 15% of your total AS marks and are examined directly in written papers—especially in Paper 2, Section A (20 marks). Furthermore, mathematical skills linked to practicals account for at least 40% of the overall qualification.

Don't worry if experimental physics and uncertainties seem intimidating at first. By breaking down each concept, mastering the exact vocabulary, and following straightforward step-by-step methods, you can secure full marks in these questions.

Quick Summary of this Guide:
• The official vocabulary of measurement (accuracy, precision, errors).
• How to calculate and combine uncertainties step-by-step.
• Comprehensive breakdowns of Required Practicals 1 to 6.
• Graphing rules, lines of worst fit, and common examiner traps.

Section 1: The Language of Measurement

Physics is an experimental science based on measurement. To describe measurements correctly, AQA requires you to use specific terms with exact scientific meanings. Misusing everyday words like "accuracy" and "precision" interchangeably is one of the most common ways students lose marks!

Key Definitions You Must Know

• True Value: The value that would be obtained in an ideal measurement where no errors exist.
• Accuracy: A measurement result is considered accurate if it is close to the true value.
• Precision: The closeness of agreement between independent measurements obtained under stipulated conditions. Precision depends only on the distribution of random errors; it does not relate to the true value.
• Resolution: The smallest change in the quantity being measured that gives a recognizable change in the reading of the instrument (for example, a standard metre rule has a resolution of \(1\text{ mm}\)).
• Repeatability: The precision obtained when test results are gathered with the same method on identical test items in the same laboratory by the same operator using the same equipment within short intervals of time.
• Reproducibility: The precision obtained when test results are gathered with the same method on identical test items in different laboratories with different operators using different equipment.

Understanding Errors: Random vs Systematic

In physics, an "error" is not a human blunder or clumsy mistake—it is a physical limitation inherent in taking measurements.

1. Random Errors:
These cause readings to be spread unpredictably about the true value. They arise from environmental changes, background noise, or human reaction time variations.
• How to reduce random errors: Take repeat readings (at least 3), discard any obvious anomalies, and calculate a mean. You can also plot a graph and draw a line of best fit.

2. Systematic Errors:
These cause readings to differ from the true value by a consistent amount each time a measurement is made.
• Common causes: Zero errors (e.g. a micrometer reading \(0.02\text{ mm}\) when fully closed), incorrect calibration, or persistent parallax error.
• How to deal with systematic errors: Repeating measurements does NOT eliminate systematic errors! You must recalibrate the instrument, subtract the zero offset from every reading, or improve the experimental technique (e.g. using a set square to avoid parallax).

Everyday Analogy: The Dartboard:
Imagine throwing darts at a bullseye (the true value):
• High precision, low accuracy: All darts are tightly clustered together, but in the top-left corner far from the bullseye (systematic error present).
• High accuracy, low precision: Darts are spread out across the board, but their average position is right at the centre.
• High accuracy, high precision: All darts are tightly grouped right inside the bullseye!

Key Takeaway for Section 1: High precision means small spread (repeatable); high accuracy means close to the true value. Repeating readings reduces random error, but only zero-correction and calibration fix systematic error.

Section 2: Calculating and Combining Uncertainties

Every experimental reading has an associated uncertainty representing the range within which the true value is expected to lie.

1. Uncertainty in Instruments

• Single reading (one-point measurement, e.g. thermometer, top-pan balance):
\(\text{Uncertainty} = \pm \frac{1}{2} \times \text{resolution}\)
Example: A thermometer with \(1\ ^\circ\text{C}\) divisions has an uncertainty of \(\pm 0.5\ ^\circ\text{C}\).

• Measurement of a length (difference between two readings, e.g. ruler):
Because you must align both the zero mark and the end mark, there is an uncertainty at both ends.
\(\text{Uncertainty} = \pm 1 \times \text{smallest scale division}\)
Example: A metre rule has divisions of \(1\text{ mm}\), so the uncertainty in a measured distance is \(\pm 1\text{ mm}\).

2. Uncertainty from Repeated Readings

When you have repeated measurements, first inspect the data and discard anomalies. Then apply the formula:
\(\text{Absolute Uncertainty} = \frac{\text{Range}}{2} = \frac{x_{\text{max}} - x_{\text{min}}}{2}\)

3. Percentage Uncertainty

To find the relative size of an uncertainty compared to the measured quantity:
\(\text{Percentage Uncertainty} = \left( \frac{\text{Absolute Uncertainty}}{\text{Mean Value}} \right) \times 100\%\)

4. Rules for Combining Uncertainties

When you calculate derived quantities, uncertainties combine according to strict algebraic rules:

Rule A: Addition and Subtraction (\(y = a + b\) or \(y = a - b\))
Add the absolute uncertainties together:
\(\Delta y = \Delta a + \Delta b\)

Rule B: Multiplication and Division (\(y = a \times b\) or \(y = \frac{a}{b}\))
Add the percentage uncertainties together:
\(\% \Delta y = \% \Delta a + \% \Delta b\)

Rule C: Powers (\(y = a^n\))
Multiply the percentage uncertainty by the power \(|n|\):
\(\% \Delta y = |n| \times \% \Delta a\)

Worked Example: Area of a Wire:
A wire diameter is measured as \(d = 0.40\text{ mm} \pm 0.01\text{ mm}\).
Step 1: Calculate \(\% \Delta d = \left(\frac{0.01}{0.40}\right) \times 100\% = 2.5\%\).
Step 2: Cross-sectional area is \(A = \frac{\pi d^2}{4}\). The power of \(d\) is \(2\).
Step 3: \(\% \Delta A = 2 \times \% \Delta d = 2 \times 2.5\% = 5.0\%\).
Examiner Warning: Never forget to double the percentage uncertainty when finding the cross-sectional area from diameter!

5. Uncertainties on Graphs (Error Bars & Worst Acceptable Lines)

• Error Bars: Plotted vertically or horizontally through a data point to show \(\pm\) the absolute uncertainty.
• Line of Best Fit: A straight line passing evenly through all error bars.
• Worst Acceptable Line: The steepest or shallowest straight line that still passes through all error bars.
• Uncertainty in Gradient:
\(\text{Absolute Uncertainty in Gradient} = |\text{Gradient of Best-Fit Line} - \text{Gradient of Worst-Fit Line}|\)
• Uncertainty in \(y\)-Intercept:
\(\text{Absolute Uncertainty in Intercept} = |y\text{-intercept of Best-Fit} - y\text{-intercept of Worst-Fit}|\)

Key Takeaway for Section 2: For addition/subtraction, add absolute uncertainties. For multiplication/division, add percentage uncertainties. For powers, multiply percentage uncertainty by the exponent.

Section 3: The 6 Required Practicals for AS Physics

Required Practical 1: Stationary Waves on a String

Aim: Investigating how the resonant frequency of stationary waves on a string varies with length (\(L\)), tension (\(T\)), and mass per unit length (\(\mu\)).

Governing Equation:
\(f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}\)

Apparatus & Setup:
A signal generator connected to a vibration generator. One end of a string is attached to the vibrator; the other passes over a wooden bridge and pulley to a mass hanger providing tension \(T = mg\).

Method & Analysis:
1. Varying Length: Keep \(T\) and \(\mu\) constant. Move the bridge to change \(L\). Adjust the frequency until the first harmonic (fundamental mode with 1 loop) is observed. Measure the distance \(L\) between the vibrator and the bridge with a metre rule.
Plot \(f\) against \(\frac{1}{L}\). The graph is a straight line through the origin with gradient \(\frac{1}{2}\sqrt{\frac{T}{\mu}}\).
2. Varying Tension: Keep \(L\) and \(\mu\) constant. Change suspended mass to vary \(T\). Find the fundamental frequency \(f\).
Plot \(f^2\) against \(T\). The gradient is \(\frac{1}{4L^2\mu}\).
3. Varying Mass per Unit Length: Use different string thicknesses/materials. Measure total mass on a balance and length with a ruler to find \(\mu = \frac{m}{L}\).
Plot \(f\) against \(\frac{1}{\sqrt{\mu}}\).

Key Practical Techniques & Error Reduction:
• Resonant nodes are sharpest when amplitude is maximized; observe the node at the bridge carefully to ensure accurate frequency tuning.
• Measure string length \(L\) using a metre rule placed parallel to the string to avoid parallax.

Required Practical 2: Investigation of Interference Effects

Aim: Investigating wave interference using (A) Young's Double-Slit experiment and (B) a Transmission Diffraction Grating.

Part A: Young's Double-Slit Experiment
• Equation: \(w = \frac{\lambda D}{s}\)
Where \(w\) is fringe spacing, \(\lambda\) is wavelength, \(D\) is distance from slits to screen, and \(s\) is slit separation.
• Method: Shine a monochromatic laser beam perpendicularly at double slits of known separation \(s\). Project the interference fringes onto a screen a distance \(D\) (at least \(1\text{ to }2\text{ m}\)) away.
• Measuring Fringe Spacing: Measure across a large number of bright fringes (e.g. \(n = 10\) fringes) using a metre rule or vernier caliper, then divide by \(n\) to find \(w\). This dramatically reduces percentage uncertainty!
• Graph: Plot \(w\) against \(D\). The gradient is \(\frac{\lambda}{s}\). Calculate wavelength \(\lambda = s \times \text{gradient}\).

Part B: Diffraction Grating
• Equation: \(d\sin\theta = n\lambda\)
Where \(d\) is grating spacing (\(d = \frac{1}{\text{lines per metre}}\)), \(\theta\) is the angle of the \(n\)-th order maximum, and \(n\) is the order number.
• Method: Direct the laser through the grating towards a screen. Measure the distance from grating to screen (\(D\)) and the distance from the central maximum (\(n=0\)) to the \(n\)-th order maxima (\(h_n\)).
• Calculating Angle: Use trigonometry: \(\tan\theta = \frac{h_n}{D}\), so \(\theta = \arctan\left(\frac{h_n}{D}\right)\).
• Graph: Plot \(\sin\theta\) against \(n\). The gradient is \(\frac{\lambda}{d}\). Wavelength is \(\lambda = d \times \text{gradient}\).

Safety Note: Lasers can cause permanent retinal damage. Never look directly into the beam; avoid reflective surfaces; display a laser warning sign.

Required Practical 3: Determination of \(g\) by a Free-Fall Method

Aim: Determining the acceleration due to gravity (\(g\)) by measuring the time taken for an object to fall through known heights.

Governing Equation:
From \(s = ut + \frac{1}{2}at^2\), starting from rest (\(u = 0\)):
\(h = \frac{1}{2}gt^2 \implies \frac{2h}{t} = gt\)

Apparatus & Setup:
• Method A (Electromagnet and Trapdoor): An electromagnet holds a steel ball. When current cuts off, a timer starts; when the ball hits the trapdoor, the switch opens and the timer stops.
• Method B (Light Gates): A card of known length or a small ball drops through two light gates connected to a digital data logger.

Analysis & Error Minimisation:
1. Measure height \(h\) from the bottom of the ball to the trapdoor using a metre rule and set square.
2. Record time \(t\) for at least 5 different drop heights, repeating each height 3 times to find a mean.
3. Plot \(h\) against \(t^2\). Gradient \(= \frac{1}{2}g \implies g = 2 \times \text{gradient}\).
(Alternatively, plot \(\frac{2h}{t}\) against \(t\), where gradient \(= g\)).
• Why Light Gates / Electronic Timers? Human reaction time (\(\approx 0.2\text{ s}\)) introduces massive percentage uncertainty over short fall times. Automated timers eliminate human reaction time.

Required Practical 4: Determination of the Young Modulus

Aim: Determining the Young modulus (\(E\)) of a metal wire by applying tensile stress and measuring tensile strain.

Governing Equations:
\(\text{Tensile Stress} = \frac{F}{A} = \frac{mg}{\frac{\pi d^2}{4}}\)
\(\text{Tensile Strain} = \frac{\Delta L}{L}\)
\(\text{Young Modulus } E = \frac{\text{Stress}}{\text{Strain}} = \frac{F L}{A \Delta L} = \frac{mg L}{\left(\frac{\pi d^2}{4}\right)\Delta L}\)

Apparatus & Procedure:
1. Clamp a long, thin wire (typically \(L \approx 2\text{ to }3\text{ m}\)) securely to a bench over a pulley.
2. Attach a paper fiducial marker to the wire near a fixed tape measure or ruler.
3. Measure the unstretched length \(L\) using a metre rule.
4. Measure wire diameter \(d\) using a micrometer screw gauge at 3 different positions and in different orientations; calculate the mean diameter to find \(A = \frac{\pi d^2}{4}\).
5. Add masses in increments of \(100\text{ g}\) (\(F = mg\)), recording the extension \(\Delta L\) via marker movement on the ruler.
6. Unload masses to confirm the wire returns to its original length (ensuring deformation remains within the elastic limit).

Analysis:
Plot mass \(m\) (or force \(F\)) against extension \(\Delta L\).
\(\text{Gradient} = \frac{F}{\Delta L}\)
\(E = \text{Gradient} \times \frac{L}{A}\)

Safety & Precision Tips:
• Wear safety goggles to protect eyes in case the wire snaps under tension.
• Use a long, thin wire to maximize \(\Delta L\) for a given load, minimizing percentage uncertainty in extension.

Required Practical 5: Determination of Resistivity of a Wire

Aim: Determining the resistivity (\(\rho\)) of a metal wire (such as nichrome or constantan).

Governing Equation:
\(R = \frac{\rho L}{A} \implies R = \left(\frac{\rho}{A}\right)L\)

Apparatus & Circuit:
A DC power supply, switch, ammeter (in series), voltmeter (in parallel across test wire length \(L\)), rheostat/resistor, and flying lead with crocodile clip connected to the test wire taped to a metre rule.

Method & Analysis:
1. Measure the wire diameter \(d\) at several points using a micrometer screw gauge; calculate the mean diameter and area \(A = \frac{\pi d^2}{4}\).
2. Connect the crocodile clip at various lengths \(L\) (e.g. \(0.20\text{ m}, 0.40\text{ m}, 0.60\text{ m}, 0.80\text{ m}, 1.00\text{ m}\)).
3. For each length, close the switch briefly, record current \(I\) and voltage \(V\), and immediately open the switch. Calculate \(R = \frac{V}{I}\).
4. Plot resistance \(R\) on the \(y\)-axis against length \(L\) on the \(x\)-axis.
5. The graph is a straight line through the origin with \(\text{Gradient} = \frac{\rho}{A}\).
6. Calculate resistivity: \(\rho = \text{Gradient} \times A\).

Critical Experimental Detail:
Switch off the circuit between readings! Current causes resistive heating in the wire (\(P = I^2 R\)), which increases resistivity and introduces a systematic error into your readings.

Required Practical 6: EMF and Internal Resistance of a Cell

Aim: Determining the electromotive force (\(\mathcal{E}\)) and internal resistance (\(r\)) of a cell or battery.

Governing Equation:
\(\mathcal{E} = I(R + r) = V + Ir \implies V = \mathcal{E} - Ir \implies V = -r I + \mathcal{E}\)
Where \(V\) is terminal potential difference, \(\mathcal{E}\) is electromotive force, \(I\) is circuit current, and \(r\) is internal resistance.

Circuit & Procedure:
Connect the cell under test in series with a switch, an ammeter, and a variable resistor (rheostat). Connect a voltmeter directly across the terminals of the cell.

1. Vary the variable resistor across its range to obtain at least 6 pairs of current \(I\) and terminal pd \(V\).
2. Open the switch between readings to prevent the cell from running down and to reduce heating.
3. Plot terminal potential difference \(V\) (on the \(y\)-axis) against current \(I\) (on the \(x\)-axis).

Graph Interpretation:
Comparing \(V = -r I + \mathcal{E}\) with \(y = mx + c\):
• \(y\)-Intercept: \(\mathcal{E}\) (the electromotive force in volts).
• Gradient: \(-r\) (the magnitude of the gradient equals the internal resistance \(r\) in ohms, \(\Omega\)).

Key Takeaway for Section 3: Each required practical links an algebraic equation directly to \(y = mx + c\). Identify which variable is manipulated (\(x\)), which is measured (\(y\)), and how the gradient and intercept yield the physical constants.

Section 4: Essential Practical Techniques (AT)

AQA tests your knowledge of specific measuring instruments and techniques:

1. Micrometer Screw Gauge:
• Resolution: \(0.01\text{ mm}\).
• Proper Use: Check for zero error before measuring; close gently using the ratchet mechanism until it clicks; measure in at least 3 places along a wire and in perpendicular directions to account for non-circular cross-sections.

2. Vernier Calipers:
• Resolution: \(0.1\text{ mm}\) (\(0.01\text{ cm}\)).
• Proper Use: Check zero mark alignment; use main scale for millimetres and vernier scale for the decimal fraction.

3. Timing Techniques & Fiducial Markers:
• When measuring the period of oscillations (e.g. pendulums or mass-spring systems), time \(10\) or \(20\) complete oscillations, then divide the total time by the count \(n\). This reduces the percentage uncertainty of human reaction time by a factor of \(n\).
• Always place a fiducial marker (a reference pin) at the equilibrium position (centre), where the moving object travels at maximum speed and passes the mark in the shortest time, minimizing timing judgment errors.

4. Alignment Aids (Plumb lines & Set squares):
• Use a plumb line to establish a true vertical reference.
• Use a set square placed against a flat bench or rule to eliminate parallax error when reading heights or scales.

Section 5: Graphing Standards and Examiner Pitfalls

Official Graphing Rules

• Axes & Labels: Always write column headings and graph axes as \(\text{Quantity } / \text{ Unit}\) (e.g. \(L\ /\ \text{m}\), \(I\ /\ \text{A}\), \(V\ /\ \text{V}\)).
• Scale: Scales must use simple multiples (\(1, 2, 5 \times 10^k\)). Plotted points must occupy more than 50% of the grid along both axes.
• Plotting: Plot points accurately using small crosses (\(\times\)) or circled dots (\(\odot\)).
• Gradient Triangle: Always draw a large gradient triangle where the hypotenuse spans at least half the length of your drawn line of best fit.

Top 7 Pitfalls to Avoid in the Exam

1. Saying "digital is more accurate": Digital meters provide higher resolution, not necessarily higher accuracy.
2. Forgetting power factors in uncertainties: For \(A = \frac{\pi d^2}{4}\), the percentage uncertainty in area is \(2 \times \% \Delta d\).
3. Including anomalies in the mean: Always cross out anomalies before adding values and calculating \(\frac{\text{sum}}{n}\) or \(\frac{\text{range}}{2}\).
4. Small gradient triangles: Drawing tiny calculation triangles loses method marks immediately.
5. Missing zero errors: If a micrometer has a zero error of \(+0.03\text{ mm}\), you must subtract \(0.03\text{ mm}\) from every raw reading.
6. Leaving circuits switched on: Heating changes resistance and compromises ohmic assumptions.
7. Inconsistent decimal places in tables: Raw data in a table column must all have the same number of decimal places, matching the resolution of the instrument used.

Quick Review: Essential Formulae Summary

• Uncertainty in repeats: \(\Delta x = \frac{x_{\text{max}} - x_{\text{min}}}{2}\)
• Stationary waves: \(f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}\)
• Double-slit interference: \(w = \frac{\lambda D}{s}\)
• Diffraction grating: \(d\sin\theta = n\lambda\)
• Free-fall acceleration: \(h = \frac{1}{2}gt^2\)
• Young Modulus: \(E = \frac{FL}{A\Delta L}\)
• Resistivity: \(R = \frac{\rho L}{A}\)
• EMF and Internal Resistance: \(V = -rI + \mathcal{E}\)

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

What is the difference between accuracy and precision in physics measurements?

Accuracy describes how close a measured value is to the true value, whereas precision describes the closeness of agreement among repeated independent measurements (reflecting only random error spread).

How do random and systematic errors differ in their causes and remediation?

Random errors cause unpredictable scatter around the true value and are reduced by repeating readings and taking a mean. Systematic errors shift readings by a constant amount and cannot be reduced by repeats; they require recalibration, zero-offset correction, or improved technique.

How do you calculate absolute uncertainty for a single reading versus repeated measurements?

For a single point reading, ext{uncertainty} = rac{1}{2} imes ext{resolution} (or ext{full division} for two-end measurements like a ruler). For repeated readings: ext{absolute uncertainty} = rac{ ext{range}}{2} = rac{x_{ ext{max}} - x_{ ext{min}}}{2} after discarding anomalies.

What are the algebraic rules for combining uncertainties when adding, multiplying, and raising to powers?

For addition/subtraction ( \(y = a \pm b\)), add absolute uncertainties: \(\Delta y = \Delta a + \Delta b\). For multiplication/division (\(y = ab\) or \(y = a/b\)), add percentage uncertainties: \(\%\Delta y = \%\Delta a + \%\Delta b\). For powers (\(y = a^n\)), multiply percentage uncertainty by \(|n|\): \(\%\Delta y = |n| \times \%\Delta a\).

In Required Practical 1 (Stationary Waves on a String), how is the relationship between frequency, length, tension, and mass per unit length analysed graphically?

Using \(f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}\): plot \(f\) against \(\frac{1}{L}\) (gradient \(= \frac{1}{2}\sqrt{\frac{T}{\mu}}\)), plot \(f^2\) against \(T\) (gradient \(= \frac{1}{4L^2\mu}\)), or plot \(f\) against \(\frac{1}{\sqrt{\mu}}\).

In Required Practical 2, how do you determine the wavelength of light using double slits and a diffraction grating?

For double slits: measure fringe spacing \(w\) over multiple fringes and use \(w = \frac{\lambda D}{s}\) (gradient of \(w\) vs \(D\) is \(\frac{\lambda}{s}\)). For a diffraction grating: use \(d\sin\theta = n\lambda\) (gradient of \(\sin\theta\) vs \(n\) is \(\frac{\lambda}{d}\)).

In Required Practical 3 (Free-Fall Method for \(g\)), why are electronic timers used and how is \(g\) extracted from a graph?

Electronic timers/light gates eliminate human reaction time error. Plotting drop height \(h\) against \(t^2\) yields a straight line with \(\text{gradient} = \frac{1}{2}g\), so \(g = 2 \times \text{gradient}\).

In Required Practical 4 (Young Modulus), what measurements are required and how is the Young modulus calculated?

Measure unstretched length \(L\) (ruler), diameter \(d\) (micrometer at multiple points for area \(A\)), and extension \(\Delta L\) for added forces \(F\). Then \(E = \text{gradient of } F\text{-}\Delta L\text{ graph} \times \frac{L}{A}\).

In Required Practical 5 (Resistivity of a Wire), how is resistivity determined and why must the switch be opened between readings?

Resistivity is calculated as \(\rho = \text{gradient} \times A\) from a graph of resistance \(R\) against length \(L\). The switch must be opened between readings to prevent resistive heating (\(I^2R\)), which alters resistance and introduces systematic error.

In Required Practical 6, how do the gradient and \(y\)-intercept of a \(V\) versus \(I\) graph give EMF (\(\mathcal{E}\)) and internal resistance (\(r\))?

From \(V = -rI + \mathcal{E}\), plotting terminal pd \(V\) against current \(I\) gives a line where the \(y\)-intercept \(= \mathcal{E}\) (EMF) and the gradient \(= -r\) (so internal resistance \(r = -\text{gradient}\)).

Why are fiducial markers placed at the equilibrium position when timing oscillations?

At the equilibrium position, the oscillating object moves at maximum speed and passes the marker in the shortest time, minimizing judgment error and reaction time uncertainty.

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