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Physics 06254.2

Electrical quantities

Charge, current, potential difference, resistance, Ohm's law and electrical energy and power.

Review these first

Learning objectives

What you need to be able to do

Teacher-mapped phrasing — check against the official Cambridge syllabus for exact wording.

  • 4.2.1Define current as charge per unit time and recall and use I = Q / t.
  • 4.2.2Define potential difference as energy transferred per unit charge and recall and use V = W / Q.
  • 4.2.3Recall and use V = IR and describe an experiment to determine resistance.
  • 4.2.4Recall and use P = IV and E = IVt.
  • 4.2.5Describe how the resistance of a wire depends on its length and cross-sectional area.Supplement

8 minute read

Current, voltage and resistance

The three quantities, defined properly

Current is the rate of flow of charge: I = Q / t, in amperes. One ampere is one coulomb per second. In a metal, the charge carriers are free electrons.

Potential difference (voltage) is the energy transferred per unit charge: V = W / Q, in volts. One volt is one joule per coulomb. This definition earns marks that "voltage is the push" never will.

Resistance is the opposition to current: R = V / I, in ohms.

Ohm's law

For a metallic conductor at constant temperature, current is directly proportional to potential difference. That "constant temperature" condition matters: a filament lamp does not obey Ohm's law because it heats up, and its I–V graph curves.

Three I–V graphs you should recognise:

  • Resistor at constant temperature: straight line through the origin.
  • Filament lamp: S-shaped curve, flattening as it heats up (resistance increases).
  • Diode: near-zero current in reverse, then rising sharply in the forward direction.

Resistance of a wire

Resistance increases with length and decreases with cross-sectional area. A long thin wire has the most resistance.

Power and energy

P = IV and, combining with V = IR, P = I²R. Energy transferred is E = IVt, or simply power × time.

This is why household appliances are rated in watts, and why kettles draw a large current: high power at a fixed mains voltage means high current.

Think of it like this

A circuit is a water loop: current is the flow rate, potential difference is the pump pressure, and resistance is a narrow pipe. Narrowing the pipe (more resistance) reduces the flow for the same pressure.

Worked examples

Method, step by step

A current of 0.25 A flows through a 48 Ω resistor. Calculate the potential difference across it.

  1. 1V = IR
  2. 2V = 0.25 × 48

V = 12 V

A 2.4 kW heater is connected to a 240 V supply. Calculate the current and the energy transferred in 5.0 minutes.

  1. 1P = IV, so I = P / V = 2400 / 240 = 10 A
  2. 2E = Pt, with t = 5.0 × 60 = 300 s
  3. 3E = 2400 × 300

I = 10 A, E = 720 000 J (720 kJ)

Common misconceptions

  • Saying current is "used up" as it goes round a series circuit. Current is the same at every point in a single loop.
  • Believing every component obeys Ohm's law. A filament lamp and a diode do not.
  • Confusing potential difference *across* a component with current *through* it — voltmeters go in parallel, ammeters in series.

In the exam

  • When asked to define potential difference, use "energy transferred per unit charge" — the everyday word "push" earns nothing.
  • For circuit diagram questions, draw the ammeter in series and the voltmeter in parallel with the component. This is a frequent easy mark.
  • State the constant-temperature condition whenever you quote Ohm's law.