Why is the energy stored ½QV and not QV?

Because the p.d. across the capacitor grows from zero as charge accumulates. The first coulomb moves through almost no p.d.; the last moves through the full V. The average is V/2, so the total work is ½QV — the area under the Q-V graph.

What does the time constant tell you?

τ = RC sets the pace of the exponential: after each interval of τ, the remaining charge falls by the same factor of e (to about 37%). A large resistance or capacitance means a slow discharge.

Why do capacitor combination rules look inverted compared to resistors?

In parallel, capacitor plates effectively add area, so capacitances add. In series, the same charge sits on each capacitor while the p.d.s add, which forces the reciprocal rule. Working from C = Q/V in each layout derives both rules in two lines.

← Edexcel IAL Physics revision

Edexcel IAL Physics revision · A2 — Fields

Capacitance

A compact topic with two halves: the algebra of storing charge (and the ½ in the energy formula), and the exponential decay of discharge — A2's gentlest introduction to the mathematics that nuclear physics will reuse.

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What the syllabus demands

—Define capacitance C = Q/V for capacitors and isolated conductors
—Derive and use the energy stored: W = ½QV = ½CV²
—Combine capacitors in series and parallel (rules opposite to resistors)
—Analyse discharge through a resistor: exponential decay, time constant τ = RC
—Use x = x₀e^(−t/RC) for charge, current and voltage

Definitions that earn marks

Clear definitions to practise — check your course mark scheme

Capacitance: The charge stored per unit potential difference: C = Q ÷ V. Units: farads (F).
Time constant (τ): τ = RC: the time for the charge (or current, or p.d.) of a discharging capacitor to fall to 1/e (about 37%) of its initial value.

The equations

CapacitanceC = Q ÷ V · F

Energy storedW = ½QV = ½CV² · J

Parallel combinationC = C₁ + C₂

Series combination1/C = 1/C₁ + 1/C₂

DischargeQ = Q₀ e^(−t/RC)

More equations to practise: the Edexcel IAL formula sheet.

Where the marks die

Common mistakes to check

01
Forgetting the ½ in the energy formula. W = QV is the energy to move charge Q through a FIXED p.d.; a capacitor's p.d. grows as it charges, so the stored energy is the area under the Q-V line: ½QV.
02
Using resistor rules for capacitors. They are opposite: capacitors in parallel ADD; in series the reciprocals add. Check your answer's size — series combinations are smaller than the smallest capacitor.
03
Misreading the time constant as 'time to fully discharge'. Exponential decay never finishes; τ is the time to fall to 37%, and 5τ is the practical 'almost empty' rule of thumb.
04
Logarithm errors when solving for t: from Q = Q₀e^(−t/RC), t = RC ln(Q₀/Q) — the ratio inside the log is initial over final.

One worked example, done properly

Question

A 470 μF capacitor charged to 12 V discharges through a 10 kΩ resistor. Find the time constant and the p.d. after 7.0 s.

Method

1.τ = RC = 10,000 × 470 × 10⁻⁶ = 4.7 s.
2.V = V₀e^(−t/τ) = 12 × e^(−7.0/4.7) = 12 × e^(−1.49).

τ = 4.7 s; V ≈ 2.7 V

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