Current and circuits

Physics · The particulate nature of matter. 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

Current is the rate of flow of charge. The emf of a cell is the energy it gives to each coulomb of charge. Potential difference is the energy each coulomb transfers in a component. Resistance is the ratio V/I. It is constant for an ohmic conductor, but it rises in a filament lamp as the lamp gets hotter.

Two conservation laws solve every circuit. Charge is conserved, so the current into a junction equals the current out. Energy is conserved, so round any loop the emfs equal the sum of the potential differences.

A real cell has internal resistance, so some volts are lost inside it and the terminal potential difference falls when the current rises. A potential divider shares the supply voltage in the ratio of the resistances.

Rules to remember

Common mistake

Students forget to convert units in the resistivity equation. An area in mm2 must be multiplied by 10−6 to give m2, and doubling the diameter makes the area four times larger, not two.

Worked example

A cell of emf 9.0 V and internal resistance 1.0 Ω is connected to two 10 Ω resistors that are in parallel with each other. What power is dissipated in each resistor?

  1. External resistance: 1/R = 1/10 + 1/10, so R = 5.0 Ω.
  2. Current from the cell: I = ε ÷ (R + r) = 9.0 ÷ (5.0 + 1.0) = 1.5 A.
  3. Terminal potential difference: V = ε − Ir = 9.0 − 1.5 × 1.0 = 7.5 V, and this is across each resistor.
  4. Power in each: P = V2 ÷ R = 7.52 ÷ 10 = 56.25 ÷ 10 = 5.6 W.

Answer: About 5.6 W in each resistor.

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