The big idea: Power is how fast electrical energy is turned into other forms — heat, light, motion.
When a current flows through a component, the component transfers energy every second. That rate is its power.
Unit: the watt (W) — 1 watt = 1 joule of energy every second.
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Spot it: Bigger current or bigger voltage → more power.
The simplest form is P = I × V (current times voltage). A 12 V supply driving 2 A delivers 12 × 2 = 24 W.
Power is current × voltage. Using Ohm's law (V = IR) you can swap V or I out, giving three equal forms of the same equation:
- electrical power (watts, W)
- current (amperes, A)
- potential difference / voltage (volts, V)
- resistance (ohms, Ω)
Which form do I use?: Choose the form using the two quantities you already know, so you don't have to find a third first:
| You know… | Use this form | Why |
|---|---|---|
| I and V | P = IV | both are given directly |
| I and R | P = I²R | no need to find V first |
| V and R | P = V²/R | no need to find I first |
Ohm's law links them: All three forms come from P = IV combined with V = IR (resistance). V = IR is also given in the data booklet.
- potential difference / voltage (volts, V)
- current (amperes, A)
- resistance (ohms, Ω)
Worked example — power from V and R
A 24 Ω heater element is connected across a 12 V supply. Find the power it dissipates.
Solution
- You know V and R, so pick the matching given form:
- Put in the numbers (V = 12, R = 24):
- Work it out — keep the unit:
Final answer
P = 6.0 W.
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How this is tested: On Paper 1A, power is usually a 'determine' question — and almost always a ratio, not a one-off number.
- Paper 1A: compare the power of two components when something changes — e.g. a wire twice as long, or a switch opened/closed that changes the voltage or current. - Paper 2: plug numbers into P = IV / I²R / V²/R, or find the energy E = Pt and the cost of running an appliance.
Classic trap: picking the wrong form. If the voltage stays fixed, use P = V²/R (P ∝ 1/R); if the current stays fixed, use P = I²R (P ∝ R). They pull opposite ways.
Resistance of a wire: For a wire of the same metal and thickness, resistance is proportional to its length: a wire twice as long has twice the resistance (R ∝ L). Combine that with the right power form to get the ratio.
IB-style question — same supply, a longer wire
Two heating wires are made of the same metal with the same thickness, and each is connected across the same 6.0 V supply. Wire 2 is twice as long as wire 1. Determine the ratio of the power dissipated in wire 2 to that in wire 1.
Solution
- The voltage is the same for both, so use the form with V and R:
- Same V means P depends only on R, and twice the length means twice the resistance (R ∝ L), so R₂ = 2R₁:
- Put in R₂ = 2R₁:
Final answer
P₂ : P₁ = 1 : 2 — the longer wire has more resistance, so at a fixed voltage it dissipates HALF the power.