Capacitance and energy storedEdexcel International A Level Physics: Revision notes

Section 1

Capacitance

A capacitor stores charge when a p.d. is applied across it. The capacitance C is the charge stored per unit potential difference:

C = Q/V

It is measured in farads (F), where 1 F = 1 C V⁻¹. Typical capacitors are microfarads (10⁻⁶ F) or millifarads. When a capacitor is charged to p.d. V, one plate carries +Q and the other −Q, and Q is directly proportional to V, so the graph of Q against V is a straight line through the origin.

Worked example: 470 μF at 12 V stores Q = 470 × 10⁻⁶ × 12 = 5.6 × 10⁻³ C.

Key termscapacitancefarad

Common mistake

Convert μF to F (10⁻⁶) before substituting into Q = CV.

Section 2

Energy stored: the area under the graph

Charging a capacitor means doing work to push charge onto a plate against the p.d. already there. Adding a small charge ΔQ when the p.d. is V needs work VΔQ, which is the area of a thin strip on a graph of V against Q.

The total energy stored is therefore the area under the V–Q graph. Because V is proportional to Q, the graph is a straight line through the origin and the area is a triangle:

W = ½QV

Key termsenergy stored

Exam tip

The ½ appears because the p.d. rises from 0 to V as the capacitor charges, so the average p.d. is V/2.

Section 3

Three energy equations

Using Q = CV, the energy can be written three ways:

W = ½QV = ½CV² = Q²/2C

Choose the form that uses the data given. For fixed C the energy is proportional to V² (halving V gives one quarter) and, for fixed C, proportional to Q².

Worked example: a camera flash capacitor of 1500 μF at 300 V stores W = ½ × 1500 × 10⁻⁶ × 300² = 67.5 J.

Common mistake

The energy is ½QV, not QV. Half the work done by the supply is stored; do not forget the ½.

Section 4

Using energy and charge together

Rearranging gives other quantities. For a stored energy W on a capacitance C, V = √(2W/C) and Q = √(2WC). For the same energy, a smaller capacitance needs a larger p.d. and holds less charge.

When a capacitor discharges, its stored energy is transferred to other forms (for example light and thermal energy in a flash lamp). The average power is W/t for a discharge time t.

Must know

C = Q/V, in farads (C V⁻¹)
W = ½QV from the area under the V–Q graph
W = ½CV² and W = Q²/2C
W ∝ V² for fixed C
Convert μF and mC to F and C

That's the notes covered.

Carry on to the next subtopic.

Exam questions on Capacitance and energy stored

A capacitor of capacitance 470 μF is connected across a 12 V d.c. supply until it is fully charged.
The capacitor is now charged using a 6.0 V supply instead of 12 V. Calculate the energy stored and explain why it is not half of the energy stored at 12 V.2 marks
The flash unit of a camera contains a capacitor of capacitance 1500 μF. It is charged to a p.d. of 300 V and then discharged through the flash lamp in a pulse lasting 1.0 ms.
Calculate the average power delivered to the flash lamp during the pulse.2 marks
A capacitor stores a charge of 2.4 mC when the potential difference across it is 8.0 V. The p.d. across a capacitor is directly proportional to the charge stored on it.
Use a graph of potential difference against charge stored to derive an expression for the energy stored in the capacitor in terms of Q and V.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).