Power in electrical circuits

By the end of this lesson

By the end you can define electrical power as rate of energy transfer, derive and use P = VI = I²R = V²/R, and calculate power in circuit components.

P = VI = I²R = V²/R — the three equivalent forms for electrical power.

Power — rate of energy transfer

Power (P) is the rate at which energy is transferred:

$P = \frac{W}{t}$

Unit: watt (W) = joule per second (J s⁻¹).

From the energy lesson: W = VIt. Substitute:

$P = \frac{V I t}{t} = V I$

P = VI — power = potential difference × current.

Alternative power formulas (using Ohm's law)

For ohmic conductors (where V = IR), we can substitute to get two more forms:

Formula	Derivation	When to use
P = V I	Definition: P = W/t, W = VIt	Always — any component
P = I²R	P = VI, substitute V = IR	When you know I and R
P = V²/R	P = VI, substitute I = V/R	When you know V and R

Important: $P = VI$ applies to any component — bulbs, motors, LEDs, batteries. The other two come from substituting $V = IR$ , so they need the resistance at that operating point. That is straightforward for an ohmic resistor; a filament lamp's resistance changes as it heats up, so for a lamp use $P = VI$ with the measured $V$ and $I$ .

What does electrical power mean physically?

P = VI: Each coulomb gives up V joules. I coulombs pass per second. So VI joules per second = watts.
P = I²R: Current I means charge flow rate. Each coulomb collides with lattice, losing energy proportional to R. More current → much more heating (I²).
P = V²/R: Higher voltage pushes more current through R (I = V/R). Power goes as V².

Why P = I²R matters for power lines: To deliver power P, you can use high V and low I (P = VI). Low I means low I²R losses in the cables. That's why the grid uses 400 kV.

Quick check — power formulas

Multiple choiceQuestion 1 · Recall

CalculateQuestion 2 · Apply

Multiple choiceQuestion 3 · Apply

Answer the 3 questions above to continue.