Energy stored in a capacitor
Section: Capacitance | Syllabus: Cambridge AS 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 Capacitor Graph 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 Graph Since 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 = 1/2QV Using Q = CV, we derive alternative forms: W = 1/2CV^2 W = 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 Loss Question: A 10~μF capacitor is charged to 2.0 V (Q = 20~μC, Energy = 20~μJ).
It is then connected in parallel with an uncharged 20~μF capacitor. Calculate the final total energy. Solution Conservation of Charge: Total charge remains Q = 20~μC. New Capacitance: C_total = 10 + 20 = 30~μF.
New Energy: W = Q^2/2C_total = (20 × 10^-6)^22 × 30 × 10^-6 6.7 ~μJ. Observation: Energy has decreased from 20~μJ to 6.7~μJ. 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~μF charged to 2000 V) to deliver a carefully controlled shock to the heart.
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