Potential and capacitors

MDCAT Physics · Physics · Electrostatics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Electric potential at a point is the work done per unit positive charge in bringing a charge from infinity to that point. It is a scalar, so potentials from several charges add with their signs. A positive charge moves freely towards lower potential; an electron moves towards higher potential. Either way the charge gains kinetic energy equal to charge × potential difference.

The electron-volt is the energy gained by one electron moving through 1 V.

A capacitor stores charge and energy. Capacitors in parallel have the same potential difference and their capacitances add. Capacitors in series carry the same charge and combine by reciprocals, the opposite of resistors.

Rules to remember

Common mistake

Combining capacitors with the resistor rules. For capacitors it is the other way round: add them directly in parallel and use reciprocals in series.

Worked example

Capacitors of 3 μF and 6 μF are connected in series across a 12 V battery. How much energy is stored in the combination?

  1. Series: C = (3 × 6) ÷ (3 + 6) = 18 ÷ 9 = 2 μF.
  2. Energy = ½CV2 = ½ × 2 × 10−6 × 122.
  3. = 1 × 10−6 × 144 = 1.44 × 10−4 J.

Answer: 1.44 × 10−4 J

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