6.1FieldsCore

Capacitors and Energy Storage

A camera flash can dump enough energy to light a room for an instant, then recharge in seconds — far faster than any chemical battery could manage. That trick relies on nothing more exotic than two conducting plates and an insulator between them: a capacitor.

40 min Video by Mr Turnbull’s Physics Module 6.1 Capacitors

Energy Stored by Capacitors — OCR A-Level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Define capacitance and use $C = \frac{Q}{V}$
Explain qualitatively how plate area, separation and the dielectric affect capacitance
Explain why energy stored is $\frac{1}{2} Q V$ , not $Q V$
Use the equivalent energy formulae $W = \frac{1}{2} Q V = \frac{1}{2} C V^{2} = \frac{1}{2} \frac{Q ^{2}}{C}$

Capacitance

A capacitor stores charge on two conducting plates separated by an insulating dielectric. Capacitance, $C$ , is the charge stored per unit potential difference, measured in farads (F) — in practice, usually microfarads, nanofarads or picofarads.

C = \frac{Q}{V}

Capacitance.

1Use

C = \frac{Q}{V}

C = \frac{4.5 \times 1 0 ^{- 4}}{15}

Answer

C = 3.0 \times 1 0^{- 5}

F (30 µF)

Factors affecting capacitance

For a parallel-plate capacitor, capacitance increases with larger plate area, decreases with larger plate separation, and increases with a higher-permittivity dielectric between the plates.

Energy stored

A capacitor’s p.d. rises from zero as it charges, unlike a battery’s constant e.m.f. Because charge and p.d. rise together in direct proportion ( $Q = C V$ ), the energy stored is the area under a Q–V graph — a triangle, giving exactly half of $Q V$ .

W = \frac{1}{2} Q V = \frac{1}{2} C V^{2} = \frac{1}{2} \frac{Q ^{2}}{C}

Energy stored in a charged capacitor.

1Use

W = \frac{1}{2} C V^{2}

W = 0.5 \times 150 \times 1 0^{- 6} \times 1 2^{2} = 0.5 \times 150 \times 1 0^{- 6} \times 144

Answer

W \approx 0.0108

J (10.8 mJ)

Tip — The most common exam trap: writing W=QV instead of ½QV. Only use QV for the work a battery does at constant e.m.f. — a capacitor’s own stored energy is always half that.

Equation recap

C = \frac{Q}{V}

Capacitance.

W = \frac{1}{2} Q V = \frac{1}{2} C V^{2} = \frac{1}{2} \frac{Q ^{2}}{C}

Energy stored.

Common mistakes to avoid

Using W = QV for the energy stored in a capacitor.

A capacitor’s p.d. rises as it charges, so the correct energy is W = ½QV.

Thinking capacitance changes with the amount of charge currently stored.

Capacitance is fixed by the capacitor’s construction — Q and V change together, but their ratio C stays constant.

Assuming a larger plate separation increases capacitance.

A LARGER separation DECREASES capacitance.

Key takeaways

Capacitance C = Q/V.
Capacitance increases with plate area, decreases with separation, increases with a higher-permittivity dielectric.
Energy stored W = ½QV = ½CV² = ½Q²/C.

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Capacitors and Energy Storage

40 min Video by Mr Turnbull’s Physics Module 6.1 Capacitors