← Electricity and electromagnetism

Power and energy calculations

The final numeric part of a circuit question is almost always power or energy — pick the right one of three equivalent formulas rather than working harder than necessary.

Choosing the right power formula from what you are given

  • Given V and I: P = VI.
  • Given I and R (no V, or V not needed): P = I²R.
  • Given V and R (no I, or I not needed): P = V²/R.
  • All three are algebraically the same relationship (from V = IR) — pick whichever avoids an unnecessary extra calculation step.
Worked example Energy converted, with a unit trap A 6.2 Ω heating element carries a current of 1.8 A for 5.0 minutes. Calculate the energy converted to heat, in joules. Choose the formula from what is given: I and R are known, so P = I²R. P = 1.8² × 6.2 = 3.24 × 6.2 = 20.1 W. Convert time to SECONDS before using energy = Pt, since P is in watts (joules per second): t = 5.0 × 60 = 300 s. Energy = Pt = 20.1 × 300 = 6030 J. ✓ ≈ 6.0 × 10³ J. The time-unit conversion (minutes → seconds) is the step most often skipped, giving an answer 60 times too small. ✕

Charge (Q = It) is not the same question as energy (E = Pt)

A question asking "how many coulombs of charge flow" wants Q = I × t (current × time, in seconds) — it does NOT want a power or energy formula at all, since coulombs are a unit of charge, not energy. Confusing the two is easy because both use current and time, but they answer completely different questions: Q = It is about how much charge has moved; E = Pt is about how much energy has been converted.

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