CCEA GCE Physics (1210) · Unit A2 3: Practical Techniques and Data Analysis
Mini-Lesson
Practical Techniques & Data Analysis (A2)
This mini-lesson covers CCEA Unit A2 3. It builds on AS 3 and adds the two skills that only appear at A2: using the cathode ray oscilloscope (CRO) to measure voltage and frequency, and handling the exponential data that A2 physics keeps producing (capacitor discharge, radioactive decay) by taking logarithms to get a straight line.
Remember: A2 3 assesses skills, not a content list — implementing, analysis, evaluation, refinement and communication. The physics can be drawn from anywhere in the A2 course.
Press Start when you are ready.
6.1 Implementing · the CRO
The cathode ray oscilloscope
A CRO plots voltage (vertical) against time (horizontal). Two dials do all the work:
Y-gain (volts/div) — how many volts one vertical square represents.
Time-base (s/div) — how much time one horizontal square represents.
V = (vertical divisions) × (volts/div)T = (horizontal divisions for one complete cycle) × (time-base), then f = 1 / T
Count the squares — not the seconds. The dials convert divisions into volts and seconds.
Reading it right: the vertical distance from the centre line to a peak is the peak voltage; the distance from trough to peak is the peak-to-peak voltage (twice as big). For a d.c. input the trace is a flat horizontal line displaced from the centre.
Calculate
Your turn — frequency from a CRO
1On a CRO, one complete cycle of a wave spans 4.0 horizontal divisions and the time-base is set to 2.0 ms/div. Calculate the frequency of the signal.
Hz
Hint: T = 4.0 × 2.0 ms = 8.0 ms = 8.0 × 10⁻³ s. f = 1/T.
Calculate
Your turn — voltage from a CRO
2The same trace has a peak-to-peak height of 6.0 vertical divisions with the Y-gain set to 5.0 V/div. Calculate the peak voltage.
V
Hint: Peak-to-peak = 6.0 × 5.0 = 30 V. The peak voltage is half the peak-to-peak value.
Quick check
Fitting more cycles on screen
?A student wants to see more complete cycles across the CRO screen. What should they change?
6.2 Analysis · logarithms
Turning an exponential into a straight line
A2 physics is full of exponential decays. A curve is very hard to test or read a constant from — so take natural logs to get a straight line.
V = V₀e−t/CR → ln V = ln V₀ − t/CRCompare with y = mx + c: plot ln V against t. Gradient = −1/CR, intercept = ln V₀.
A = A₀e−λt → ln A = ln A₀ − λtPlot ln A against t. Gradient = −λ, and then T½ = ln 2 / λ.
Why bother? Because a straight line lets you (a) confirm the relationship really is exponential, (b) extract the constant from a gradient using all the data, not just two points, and (c) put a quantitative uncertainty on it with a line of worst fit.
Radioactive decay: always subtract the background count rate from every reading before taking logs. Forgetting to do so bends the line and gives a half-life that is too long.
Calculate
Your turn — from a log gradient
3A student plots ln V against t for a discharging capacitor and obtains a straight line of gradient −0.25 s⁻¹. The capacitor is 100 µF. Calculate the resistance, in kΩ.
kΩ
Hint: Gradient = −1/CR, so CR = 1/0.25 = 4.0 s. R = 4.0 ÷ (100 × 10⁻⁶) = 40 000 Ω.
Calculate
Your turn — half-life with background
4The background count rate is 10 counts per minute. A source reads 210 cpm, and 30 minutes later it reads 60 cpm. Calculate the half-life.
minutes
Hint: Corrected rates: 210 − 10 = 200 cpm, and 60 − 10 = 50 cpm. 200 → 100 → 50 is TWO half-lives in 30 minutes.
Quick check
Why plot ln A?
?Why do we plot ln A against t rather than A against t, when investigating radioactive decay?
Sort it
What will this actually fix?
Tap a technique, then tap what it does.
🎯 Improves precision
🛠️ Removes a systematic error
🚫 Will not help
6.3 Evaluation · uncertainty
Uncertainty in A2 experiments
The three rules from AS still do everything:
Add or subtract → add the absolute uncertainties.
Multiply or divide → add the percentage uncertainties.
Power n → multiply the percentage uncertainty by n.
Worked example — the Young modulus
E = FL / (Ae), and A = πd²/4, so d contributes twice its percentage uncertainty.
Total % uncertainty in E = 1.0 + 0.5 + 4.0 + 3.0 = 8.5%
The diameter and the extension dominate — so a micrometer and a travelling microscope (or a much longer wire) are where the improvement must come from.
Precision instruments at A2: micrometer (0.01 mm) for wire diameter · vernier calipers (0.1 mm) · digital multimeter · travelling microscope for tiny extensions · light gates and data loggers to eliminate reaction time altogether.
Calculate
Your turn — combining uncertainties
5In a Young modulus experiment, E = FL/(Ae) with A = πd²/4. The percentage uncertainties are: F 1.0%, L 0.5%, d 2.0%, e 3.0%. Calculate the total percentage uncertainty in E.
%
Hint: d appears as d², so it contributes 2 × 2.0% = 4.0%. Now add: 1.0 + 0.5 + 4.0 + 3.0.
Calculate
Your turn — uncertainty in a gradient
6A best-fit line has gradient 4.90; the line of worst fit through all the error bars has gradient 5.10. Calculate the percentage uncertainty in the gradient.