Discharging a capacitor
Cambridge A-Level Physics (9702) · Unit 19: Capacitance · 8 flashcards
Discharging a capacitor is topic 19.3 in the Cambridge A-Level Physics (9702) syllabus , positioned in Unit 19 — Capacitance , alongside Capacitors and capacitance and Energy stored in a capacitor. In one line: The time constant (τ) is the time taken for the voltage (or current, or charge) to fall to approximately 37% (1/e) of its initial value during the discharge of a capacitor. It is given by the formula τ = RC.
Marked as A2 Level: examined at A Level in Paper 4 (A Level Structured Questions) and Paper 5 (Planning, Analysis and Evaluation). It is not tested on the AS-only papers (Papers 1, 2 and 3).
The deck below contains 8 flashcards — 1 definition, 3 key concepts and 4 calculations — covering the precise wording mark schemes reward. Use the definition card to lock down command-word answers (define, state), then move on to the concept and calculation cards to handle explain, describe, calculate and compare questions.
The term 'time constant' (τ) for a capacitor discharging through a resistor. What does it physically represent
The time constant (τ) is the time taken for the voltage (or current, or charge) to fall to approximately 37% (1/e) of its initial value during the discharge of a capacitor. It is given by the formula τ = RC.
What the Cambridge 9702 syllabus says
Official 2025-2027 spec · A2 LevelThese are the exact learning outcomes Cambridge sets for this topic. The candidate is expected to be able to do each of these on the relevant paper.
- analyse graphs of the variation with time of potential difference, charge and current for a capacitor discharging through a resistor
- recall and use τ = RC for the time constant for a capacitor discharging through a resistor
- use equations of the form x = x0 e–(t / RC) where x could represent current, charge or potential difference for a capacitor discharging through a resistor
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 9702 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Tips to avoid common mistakes in Discharging a capacitor
- › Use precise terminology: capacitance is the ratio of the charge on one plate to the potential difference between the plates.
- › Apply the principle of conservation of charge; the total charge before and after redistribution must remain the same.
- › Calculate energy stored using (1/2)CV^2 for each state separately, then find the difference. Do not use (1/2)C(delta V)^2.
- › Recall that the time constant (τ = RC) has units of seconds (s).
Describe the shape of the voltage vs. time graph for a capacitor discharging through a resistor. What does the shape represent?
The voltage vs. time graph is a decreasing exponential curve. This represents the voltage decreasing over time as the capacitor discharges its stored charge through the resistor.
Define the term 'time constant' (τ) for a capacitor discharging through a resistor. What does it physically represent?
The time constant (τ) is the time taken for the voltage (or current, or charge) to fall to approximately 37% (1/e) of its initial value during the discharge of a capacitor. It is given by the formula τ = RC.
State the formula that relates the voltage (V) across a discharging capacitor to its initial voltage (V₀), time (t), resistance (R), and capacitance (C).
The voltage across a discharging capacitor is given by: V = V₀e^(-t/RC), where V₀ is the initial voltage, t is time, R is resistance, and C is capacitance.
A 100μF capacitor discharges through a 10kΩ resistor. Calculate the time constant (τ) of the circuit.
The time constant (τ) is calculated as τ = RC. Therefore, τ = (10,000 Ω) * (100 × 10⁻⁶ F) = 1 second.
If a capacitor initially charged to 12V is discharging through a resistor, what is the voltage across the capacitor after one time constant (τ)?
After one time constant, the voltage is approximately 37% of its initial value. Therefore, V = 0.368 * 12V ≈ 4.42V.
How does increasing the resistance in a discharging RC circuit affect the discharge time and the time constant?
Increasing the resistance increases the discharge time because it limits the current flow. The time constant τ = RC is directly proportional to R, so increasing R increases τ, meaning a longer time to discharge.
How does increasing the capacitance in a discharging RC circuit affect the discharge time and the time constant?
Increasing the capacitance increases the discharge time because the capacitor can store more charge. The time constant τ = RC is directly proportional to C, so increasing C increases τ, meaning a longer time to discharge.
Write the equation to describe how the charge (Q) on a discharging capacitor varies with time.
The charge (Q) on a discharging capacitor varies with time according to the equation: Q = Q₀e^(-t/RC), where Q₀ is the initial charge, t is the time, R is the resistance, and C is the capacitance.
Review the material
Read full revision notes on Discharging a capacitor — definitions, equations, common mistakes, and exam tips.
Read NotesMore topics in Unit 19 — Capacitance
Discharging a capacitor sits alongside these A-Level Physics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Key terms covered in this Discharging a capacitor deck
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