Power in Resistive Circuits — Quick Revision

Mr Toogood's Physics · Electricity basics

AQA 3.5.1.4
P = IV
Electrical power
E = IVt
Energy
P = I²R
Fixed current
P = V²/R
Fixed p.d.

Electrical power

Power is the rate of energy transfer, P = W/t, measured in watts (1 W = 1 J s⁻¹). Substituting I = Q/t and V = W/Q gives the key equation:

P = IV

Total energy transferred over time t: E = IVt. Applies to a whole circuit (using emf) or to a single component (using its p.d.).

Power & resistance — which equation?

Two resistors in series sharing the same current, showing power depends on resistance

Series resistors share the same current — power ∝ R here.

P = I²R — use when current is fixed/known (e.g. resistors in series). Power increases directly with R.
P = V²/R — use when p.d. is fixed/known (e.g. a resistor alone across the full emf, or one branch of a parallel network). Power increases as R decreases.

The two aren't contradictory — they describe different circuit conditions (what's held constant), not different physics.

Cells in series & parallel

Cells connected in series with a hill diagram showing emf adding up

Series cells: emf adds — charge gains potential through each cell in turn.

  • Series: total emf = ε₁+ε₂+⋯; current is the same as for a single cell.
  • Parallel (identical cells): emf = one cell's emf (unchanged); current capacity adds — useful for high-current demand or longer capacity (mAh).

Conservation of energy

Circuit showing power delivered by a cell equals total power dissipated by all components

Power delivered by the cell = total power dissipated by every component.

Pcell = ΣPcomponents

Every joule the cell supplies must be accounted for around the circuit — a direct consequence of Kirchhoff's 2nd law (energy conservation) applied to power.

Exam essentials

Choosing the equation

  • Know both I and V? → just use P=IV.
  • Only I given/constant? → P=I²R.
  • Only V given/constant? → P=V²/R.

Cells quick contrast

  • Series: emf sums, current unchanged.
  • Parallel: emf unchanged, current capacity sums.

Common slips

  • Convert kJ → J and s → minutes carefully in energy questions.
  • E=Pt only holds if power is constant over that time.
  • Self-check: total power out (components) should equal power in (cell) — if not, recheck your working.