Cambridge International AS & A Level · P5 · structured
Complete and analyse the semi-log table
A2 practical 7: construct a capacitor-discharge semi-log record · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 11
- Topics
- 4
- Answer
- Complete
Complete the constructed discharge table, including logarithms and their conservative uncertainty bounds using the larger of ln(U)-ln(U-Delta U) and ln(U+Delta U)-ln(U), with numerical U in volts. Draw a semi-log fit and recover tau and U0. Explain why time is not logged here, why ln(U/V) has no unit and why the original U column remains necessary. Use the measured resistor value R=1.00x10^5 ohm to obtain C assuming negligible meter loading. Justify the number of significant figures in this non-logarithmic derived C value using the least precise multiplicative input, separately from your logarithmic decimal-place justification. Constructed illustrative data (not observed experimental evidence). Columns: t / s (constructed) | U / V (constructed) | ln(U/V) | ln uncertainty (conservative endpoint bound). Rows: 0.0 ± 0.1 | 4.98 ± 0.05 | 1.6054 | ± 0.0101; 10.0 ± 0.1 | 4.08 ± 0.05 | calculate | calculate; 20.0 ± 0.1 | 3.36 ± 0.05 | calculate | calculate; 30.0 ± 0.1 | 2.74 ± 0.05 | calculate | calculate; 40.0 ± 0.1 | 2.25 ± 0.05 | calculate | calculate; 50.0 ± 0.1 | 1.84 ± 0.05 | calculate | calculate.
- (a)
Complete the raw/derived/uncertainty table.
4 marks - (b)
Plot and recover parameters; calculate C and justify its significant figures.
6 marks - (c)
Explain the transformation and record structure.
1 mark
Ready to self-mark?Reveal the detailed answer guide
(a)
Complete the raw/derived/uncertainty table.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Preserve original readings; correct six ln values, conservative bounds and appropriate3/4 dp notation.
(b)
Plot and recover parameters; calculate C and justify its significant figures.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
ln(U/V) versus t/s fit; tau about 50.2 s, U0 about 4.98 V, C about 502 microfarad; 3 or 4 sf are supported by the 3-sf resistor input and the stated fitted precision.
(c)
Explain the transformation and record structure.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Exponential law needs logarithm of response only; raw observations must remain traceable.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- All transformed values and uncertainty cells completed beside preserved raw data:3 marks.
- Justified log decimal places and dimensionless heading:1 mark.
- Correct chosen axes, all-point graph and defensible fit:2 marks.
- Large fitted-line slope/intercept and corresponding tau/U0:2 marks.
- C=tau/R with units: 1 mark. Explain that the supplied R has 3 significant figures, so 3 or 4 significant figures are appropriate for C here under the P3 multiplicative rule, assuming the fitted slope supports at least that precision: 1 mark.
- Explain exponential model linearisation and why raw values remain the traceable source:1 mark.
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