Energy stored in a capacitor
Section: Capacitance | Syllabus: Cambridge A Level Physics (9702)
Work Done and Energy
Charging a capacitor involves doing work to separate positive and negative charges. This work is stored as electric potential energy in the electric field between the plates.
Figure 19.17: Q-V Graph for a CapacitorGraph of potential difference V against charge Q showing a straight line through the origin. The shaded triangular area represents the energy stored W = ½QV.
Area under Q-V GraphSince V increases linearly with Q, the graph of V against Q is a straight line. The work done W is the area under this graph (a triangle):
W = (1/2)QVUsing Q = CV, we derive alternative forms:
W = (1/2)CV^2W = (Q^2/2C)
Common Mistake: Do not forget the (1/2) factor. W = QV only applies when moving charge through a constant potential difference.
Worked Examples
Worked Example: Energy Sharing LossQuestion: A 10~ capacitor is charged to 2.0 V (Q = 20~, Energy = 20~). It is then connected in parallel with an uncharged 20~ capacitor. Calculate the final total energy.
Solution- Conservation of Charge: Total charge remains Q = 20~.
- New Capacitance: C_total = 10 + 20 = 30~.
- New Energy: W = Q^22C_total = (20 × 10^-6)^22 × 30 × 10^-6 ≈ 6.7 ~.
Observation: Energy has decreased from 20~ to 6.7~. The "lost" energy is dissipated as heat in the wires during the flow of charge.
Applications: Flash and Defibrillators
Capacitors can discharge very rapidly, making them ideal for providing high-power bursts.
- Camera Flash: A capacitor stores energy slowly and releases it in milliseconds.
- Defibrillator: Uses a large capacitor (e.g., 200~ charged to 2000 V) to deliver a carefully controlled shock to the heart.
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