Power and Electrical Energy

Electrical power — the rate of energy transfer:

P = VI

which follows directly from the definitions: V is energy per unit charge and I is charge per unit time, so their product is energy per unit time.

The other two forms — substituting V = IR gives

P = I²R

and substituting I = V/R gives

P = V² / R

All three are the same statement. Choose whichever matches the quantities you have.

Example: a device drawing 0.50 A from a 230 V supply dissipates P = 230 × 0.50 = 115 W.

A trap worth noting — P = I²R and P = V²/R appear to disagree about whether a larger resistance means more or less power. Both are correct; they answer different questions. At constant current a larger resistance dissipates more power; at constant p.d. a larger resistance dissipates less. Before using either, decide which quantity is fixed by the circuit.

Energy transferred —

W = VIt = Pt

measured in joules when t is in seconds.

Why transmission lines run at high voltage — power lost as heat in the cables is I²R, so it depends on the square of the current. Transmitting the same power at a much higher voltage requires a proportionally smaller current, and cutting the current by a factor of ten cuts the heating loss by a factor of a hundred. The cable resistance is unchanged; only the current matters.

Fuses and ratings — a fuse is chosen so that it melts at a current slightly above the appliance's normal working current, breaking the circuit before the wiring overheats. Choosing a fuse that is too large defeats the purpose entirely, since the wiring will fail before the fuse does.