Electrostatics and current electricity

Physics · Heat, electricity and light. 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

Charges exert inverse-square forces on each other. The electric field is the force per unit positive charge and the potential is the potential energy per unit charge. Field lines run from high to low potential and cross equipotential surfaces at right angles. Gauss's law links the flux out of a closed surface to the charge inside it; with symmetry it gives the field in one line.

A capacitor stores charge and energy in the field between its plates.

In a circuit, current is the rate of flow of charge. Kirchhoff's laws express conservation of charge at a junction and conservation of energy round a loop. Every circuit problem, from series and parallel resistors to bridges, comes from these two laws and V = IR.

Rules to remember

Common mistake

Combining capacitors like resistors. Capacitances add in parallel and combine by reciprocals in series, the opposite of resistances.

Worked example

A battery of e.m.f. 18 V and internal resistance 2 Ω is connected to a 6 Ω and a 12 Ω resistor in parallel. Find the current from the battery and the terminal p.d.

  1. Parallel pair: R = (6 × 12) ÷ (6 + 12) = 72 ÷ 18 = 4 Ω.
  2. Total resistance = 4 + 2 = 6 Ω, so I = 18 ÷ 6 = 3 A.
  3. Terminal p.d. = E − Ir = 18 − 3 × 2 = 12 V.
  4. Check: 12 ÷ 6 = 2 A and 12 ÷ 12 = 1 A, which add to 3 A.

Answer: 3 A; terminal p.d. 12 V.

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