OxfordAQA International A Level Physics
OxfordAQA International A Level Physics 3.9 Exponential Change Exam Questions
Free OxfordAQA International A Level Physics revision for 3.9 Exponential Change: what you need to know, common mistakes and exam-style questions with answers. Covers capacitor charge and discharge through a resistor, time constant, half-time, exponential equations, radioactive decay constant, activity and half-life.
Practise 3.9 Exponential Change with past papers
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About OxfordAQA International A Level Physics 3.9 Exponential Change
Exponential change is part of Unit 3 (PH03), Fields and their consequences, in the OxfordAQA International A2 year. It brings together two processes that follow the same mathematics: the charging and discharging of a capacitor through a resistor, and radioactive decay. You need to use the exponential equations, the time constant RC, the decay constant and the link between half-life and these constants. It builds on capacitance from 3.8 and on half-life from 3.3. Examiners often set calculations of charge, current or pd after a given time, log-linear graph analysis to find RC or the decay constant, and questions on the required practical investigating capacitor discharge.
What you need to know
- Capacitor discharge Q = Q0 e^(-t / RC), and the current and pd follow the same form. The time constant RC is the time for the charge to fall to 1/e (about 37%) of its starting value.
- Capacitor charging Q = Q0 (1 - e^(-t / RC)); the pd across the capacitor rises quickly at first then levels off, while the current falls exponentially from its initial value V / R.
- Half-time The time for the charge to halve on discharge is T1/2 = 0.69 RC (ln 2 x RC).
- Graphical analysis Plotting ln V against t for a discharge gives a straight line with gradient -1 / RC. The area under a current-time graph gives the charge.
- Radioactive decay Activity A = lambda N, where lambda is the decay constant (probability of decay per unit time). N = N0 e^(-lambda t) and A = A0 e^(-lambda t).
- Half-life T1/2 = ln 2 / lambda. Uses of different half-lives include radioactive dating and choosing medical tracers with short half-lives.
Common mistakes in 3.9 Exponential Change
- Using a value of t in minutes with RC in seconds. Keep all times in the same units.
- Saying the capacitor is fully discharged after one time constant. After RC it still has about 37% of its charge.
- Writing lambda in s-1 but half-life in years when calculating activity. Convert half-life to seconds if activity is needed in becquerels.
- Confusing the decay constant with half-life. A larger decay constant means a shorter half-life.
- Using N0 in place of activity, or forgetting that A = lambda N links number of nuclei to activity.
Try three 3.9 Exponential Change exam-style questions
1. A 220 microfarad capacitor charged to 9.0 V discharges through a 47 kilohm resistor. Calculate the time constant and the pd after 5.0 s. (3 marks)
Show the mark scheme answer
RC = 220 x 10^-6 x 47 x 10^3 = 10.3 s; V = 9.0 e^(-5.0 / 10.3); V = 5.5 V.
2. Iodine-131 has a half-life of 8.0 days. A sample has an initial activity of 4.0 x 10^6 Bq. Calculate its activity after 20 days. (3 marks)
Show the mark scheme answer
lambda = ln 2 / 8.0 = 0.087 day-1; A = 4.0 x 10^6 x e^(-0.0866 x 20) (or 4.0 x 10^6 x 0.5^2.5); A = 7.1 x 10^5 Bq.
3. Describe how a graph can be used to find the time constant of a discharging capacitor circuit from readings of pd and time. (3 marks)
Show the mark scheme answer
Plot ln V on the y-axis against t; it gives a straight line; the gradient is -1 / RC, so RC = -1 / gradient.
3.9 Exponential Change FAQs
What does OxfordAQA International A Level Physics 3.9 Exponential Change cover?
It covers capacitor charging and discharging through a resistor, the time constant and half-time, and exponential radioactive decay with the decay constant, activity and half-life.
Which unit is 3.9 Exponential Change examined in?
It is examined in Unit 3 (PH03), Fields and their consequences.
How do I handle the e^x equations in 3.9 Exponential Change?
Practise using the e^x and ln buttons on your calculator. To find a time, take natural logs: t = -RC ln(Q / Q0) for discharge or t = -ln(A / A0) / lambda for decay.
