What happens during the discharging of a capacitor?

During the discharging of a capacitor, the stored electrical energy is released as the charge flows from the capacitor through the circuit. This process continues until the potential difference across the capacitor plates reaches zero, meaning the capacitor is fully discharged. This is a key concept in the study of capacitance in Physics, especially at the Cambridge International A Levels.

How is the time constant related to the discharging of a capacitor?

The time constant, denoted by the symbol τ (tau), is a crucial parameter in the discharging process of a capacitor. It is defined as the product of the resistance (R) and the capacitance (C) of the circuit, τ = RC. The time constant represents the time it takes for the voltage across the capacitor to decrease to approximately 37% of its initial value. Understanding the time constant is essential for Cambridge International A Levels students studying the dynamics of capacitors.

What is the formula for the voltage across a discharging capacitor over time?

The voltage V across a discharging capacitor as a function of time t is given by the formula V(t) = V₀ * e^(-t/RC), where V₀ is the initial voltage, R is the resistance, C is the capacitance, and e is the base of the natural logarithm. This exponential decay formula is fundamental in analyzing how capacitors discharge over time in Physics.

Why is it important to understand the discharging process of a capacitor in Physics?

Understanding the discharging process of a capacitor is important because it helps explain how capacitors function in electronic circuits, including their role in timing applications, filtering signals, and energy storage. This knowledge is crucial for students at the Cambridge International A Levels, as it forms the basis for more advanced studies in electronics and electrical engineering.

What factors affect the rate at which a capacitor discharges?

The rate at which a capacitor discharges is primarily affected by the resistance and capacitance of the circuit. A higher resistance or capacitance results in a slower discharge rate, as indicated by the time constant τ = RC. Additionally, the initial voltage across the capacitor also influences the discharge rate. These factors are essential for students to consider when studying capacitance and capacitor behavior in Physics.

Why is "Inconsistent units in $RC$" a common mistake in Discharging a capacitor?

Why it happens: Common. How to avoid it: R in ohms, C in farads → in seconds. Watch μF. Source: 9702 Examiner Reports 2022-2024

Discharging a capacitor – Study Notes & Past Paper Style Questions | Cambridge International A Level Physics 9702

Short Notes - Discharging a capacitor

Detailed Study Notes

Detailed notes on Capacitance for Cambridge International A Levels Physics, covering key concepts, explanations, examples, and exam-focused revision points.

Discharging Capacitor Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Exponential decay with time constant $\tau = RC$ .

At a glance

$Q(t) = Q_0 e^{-t/RC}$ .
$\tau = RC$ time constant.
$V$ and $I$ decay together with same $\tau$ .
After $\tau$ , drops to ~37%.

What you’ll learn

Mapped to the Cambridge International A Level 9702 syllabus (2025-2027).

19.3.1 — Use discharge equations.
19.3.2 — Interpret time constant.

Discharging RC circuit

Exponential decay.

Setup. Capacitor charged to $V_0$ discharges through resistor $R$ .

Equations. $Q(t) = Q_0 e^{-t/RC}$ $V(t) = V_0 e^{-t/RC}$ $I(t) = I_0 e^{-t/RC}$

Time constant. $\tau = RC$ (units: seconds).

Key fractions.

$t = \tau$ : 36.8% of initial.
$t = 2\tau$ : 13.5%.
$t = 5\tau$ : ~1%.

Half-life. $T_{1/2} = \tau \ln 2 \approx 0.693\tau$ .

Charging (covered briefly). Symmetric: $V(t) = V_0(1 - e^{-t/RC})$ rising.

Cambridge tip. Always state time constant in your working.

Figure 1 — Exponential discharge of a capacitor

During discharge Q, V and I all fall exponentially with the same time constant τ = RC. After one τ the value is 37 % of the start, after two τ it is 13.5 %.

Figure 2 — The RC discharge circuit

The capacitor acts as the source. As its charge falls, so does the p.d. driving the current — which is exactly why the decay is exponential rather than steady.

Figure 3 — Q, V and I all decay with the same time constant

Only the vertical scale differs between the three graphs. That is why an experiment can track whichever quantity is easiest to measure.

Figure 4 — Charging is the mirror image of discharging

Charging and discharging share the same time constant. The two fractions always add to one: 0.63 gained is the same event as 0.37 remaining.

Fractions to recognise during a discharge.

Time elapsed	Fraction of the starting value	Where it comes from
$t = \tau$	$0.37$ (36.8 %)	$e^{-1}$
$t = 2\tau$	$0.135$ (13.5 %)	$e^{-2}$
$t = 5\tau$	about 1 %	$e^{-5}$ — treated as fully discharged
$t = 0.693\tau$	$0.50$	the half-life, $T_{1/2} = \tau \ln 2$

Charging is the mirror image: $V = V_0(1 - e^{-t/RC})$ rises towards $V_0$ with the same time constant.

Exponential decay.
$\tau = RC$ .
$V(\tau) \approx 0.37 V_0$ .

See the full worked example for discharging a capacitor →

Quick recap

$Q = Q_0 e^{-t/RC}$ .
Time constant $\tau = RC$ .
$V$ and $I$ decay similarly.

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

Discharge formula.
$\tau = RC$ .

How it’s examined

Discharging on every Paper 4. Most-tested: time constant (5 marks), discharge value (7 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/42 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

Take this whole topic with you

Step-by-step worked examples — Discharging a capacitor

Step-by-step solutions to past-paper-style questions on discharging a capacitor, written exactly the way a tutor would explain them at the board.

1Discharge calculation (7 marks)
Extended• Adapted from 9702/42 May/Jun 2024• discharge
Question
A 100 μF capacitor charged to 12 V discharges through 10 kΩ. Find PD after 0.50 s. (7 marks)
Step-by-step solution
1. Step 1
  Time constant. $\tau = RC = 10^4 \times 100 \times 10^{-6} = 1.0$ s.
2. Step 2
  $V(t) = V_0 e^{-t/\tau}$ .
  $V(0.5) = 12 e^{-0.5/1.0} = 12 \times 0.607 \approx 7.3 \text{ V}$
Answer
$V \approx 7.3$ V.
2Time constant interpretation (5 marks)
Extended• time constant
Question
Define time constant $\tau$ . Find PD after one time constant. (5 marks)
Step-by-step solution
1. Step 1
  $\tau = RC$ . Time for $V$ to fall to $e^{-1}$ of initial.
2. Step 2
  $V(\tau) = V_0/e \approx 0.368 V_0$ . About 37% of initial.
Answer
$\tau = RC$ . $V(\tau) \approx 0.37 V_0$ .

Key Formulae — Discharging a capacitor

The formulae you need to memorise for discharging a capacitor on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Discharge equations
$Q(t) = Q_0 e^{-t/RC}, \quad V(t) = V_0 e^{-t/RC}, \quad I(t) = I_0 e^{-t/RC}$
$\tau = RC$
time constant
When to use
RC circuit discharging. All quantities decay together with same $\tau$ .

Key Definitions and Keywords — Discharging a capacitor

Definitions to memorise and the exact keywords mark schemes credit for discharging a capacitor answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Time constant
Examiner keyword
$\tau = RC$ . Time for charge/PD/current to fall to $1/e$ ( $\approx 37\%$ ) of initial value during discharge.

Common Mistakes and Misconceptions — Discharging a capacitor

The traps other students keep falling into on discharging a capacitor questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Inconsistent units in $RC$
9702 Examiner Reports 2022-2024
Why it happens
Common.
How to avoid it
$R$ in ohms, $C$ in farads → $\tau$ in seconds. Watch μF.

Discharging a capacitor — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Discharging a capacitor

Short Notes - Discharging a capacitor

Detailed Study Notes

At a glance

What you’ll learn

Discharging RC circuit

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Discharge calculation (7 marks)

2Time constant interpretation (5 marks)

Discharge equations

Time constant

✕Inconsistent units in RCRCRC

Discharging a capacitor — frequently asked questions

Discharging a capacitor

Short Notes - Discharging a capacitor

Detailed Study Notes

At a glance

What you’ll learn

Discharging RC circuit

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Discharge calculation (7 marks)

2Time constant interpretation (5 marks)

Discharge equations

Time constant

✕Inconsistent units in RCRCRC

Discharging a capacitor — frequently asked questions

✕Inconsistent units in $RC$

✕Inconsistent units in $RC$