Power in Circuits

We know that resistance turns electrical energy into heat as electrons collide with the lattice. But how fast does that energy transfer actually happen? That’s exactly what power tells us — and once we’ve pinned it down, three handy formulas fall right out of it.

What does “power” actually mean here?

Think about two identical kettles, one rated at 1000 W and the other at 2000 W. Both will eventually boil the same amount of water and transfer the exact same total amount of energy — but the 2000 W kettle does it in half the time. Power isn’t about how much energy gets transferred overall; it’s about how quickly that energy is being delivered, moment to moment.

where P is power in watts (W), E (or W) is the energy transferred in joules (J), and t is time in seconds (s). One watt simply means one joule of energy being transferred every second.

Three formulas, one idea

Remember that voltage is energy per unit charge, and current is charge per unit time. Multiply them together, and the charge cancels out, leaving you with exactly what power means — energy per unit time:

This version works for literally any component in any circuit. But since we also know V = IR from Ohm’s law, we can substitute that in to get two more useful versions — handy for whenever a question only gives you current, or only gives you voltage:

A useful way to remember this trio: for a fixed resistor, doubling the current (or the voltage) doesn’t just double the power — it quadruples it, because both formulas involve a squared term.

Total energy transferred

If we know the power and how long it’s been running for, we can work backwards to find the total energy delivered — just rearrange our very first equation: