OCR A-Level Physics B H557
Planning
Implementing
Analysis
Evaluation
Practical Skills
Use of Apparatus and Techniques
Fundamental Data Analysis
Imaging and Signalling
Sensing
Mechanical Properties of Materials
Waves and Quantum Behaviour
Space, Time and Motion
Creating Models
Out Into Space
Our Place in the Universe
Matter: Very Simple
Matter: Hot or Cold
Electromagnetism
Charge and Field
Probing Deep Into Matter
Ionising Radiation and Risk
Creating Models
Iterative numerical models of exponential change
- 3 things to know
- Components 01, 02 and 03
Overview
Recall questions on step-by-step solutions of dQ/dt = −Q/(RC) and radioactive decay, calculating single steps, why such models predict too fast a fall, improving accuracy with smaller steps and the drawback of doing so, choosing a step size, checking against N = N₀exp(−λt) and in a spreadsheet, the graphical tangent method, and negative outputs.
What you need to know
Answer each one before you reveal it.
Why does a step-by-step model of decay always predict too fast a fall?
State the recipe for one step of a numerical model of capacitor discharge.
Questions from this subtopic
Each one with the model answer underneath.
- 1
Explain the idea behind solving dQ/dt = −Q/(RC) by a step-by-step numerical method.
Model answer
The rate of change is calculated from the present charge, assumed constant over a small time step, used to find the change in charge, and the whole process is repeated from the new value.
- 2
State the recipe for one step of a numerical model of capacitor discharge.
Model answer
Compute ΔQ = −(Q/RC)Δt, add it to Q to get the new charge, advance the time by Δt and repeat.
- 3
A capacitor holds 1.0 × 10⁻³ C with R = 1.0 kΩ and C = 100 μF. How much charge is lost in a first step of 0.010 s?
Model answer
ΔQ = −(Q/RC)Δt = −(1.0 × 10⁻³ / 0.10) × 0.010 = −1.0 × 10⁻⁴ C.
- 4
A model step removes 1.0 × 10⁻⁴ C from a stored charge of 1.0 × 10⁻³ C. What is the charge at the end of that step?
Model answer
The charge is 1.0 × 10⁻³ − 1.0 × 10⁻⁴ = 9.0 × 10⁻⁴ C.
- 5
Why does a step-by-step model of decay always predict too fast a fall?
Model answer
The rate is held at its value from the start of the step, but the true rate falls during the step, so too much is subtracted each time.
- 6
How is the accuracy of an iterative model improved?
Model answer
Use a smaller time step, so that the rate changes very little during each step.
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