Electric Power: Revision Notes (Physics 2 11.4)

Short on time? This page is the recap. For the derivations, figures and worked examples, use the full study guide.

Recap

Power is the rate at which energy is transferred, converted or dissipated. Unit: watt, 1 W = 1 J/s.
P = IΔV comes from energy per charge (ΔV) multiplied by charge per second (I). It applies to every element.
Into the circuit: the battery, at a rate Iℰ for an ideal battery. Out of the circuit: resistors and bulbs, as thermal energy (and light). Within: a capacitor can store energy.
With an ideal battery, energy in per second = total energy out (and stored) per second.
Brightness of a bulb increases with its power.

Relationship	Symbols and units	Use it when
P = IΔV	W = A × V	any element, I and ΔV known
P = I²R	R in Ω	elements share the same current (one loop)
P = ΔV²/R	ΔV in V	elements share the same ΔV (each directly across the same battery)
ΔE = PΔt	J, with Δt in s	energy transferred in a time

Batteries are ideal and wires have no resistance.
Resistors and bulbs keep a constant resistance unless the question says otherwise.
A rating such as “6.0 V, 3.0 W” applies only at the stated potential difference.

“Bigger R, more power” without checking what is shared. It is true only for the same current.
Forgetting the square. Double I or ΔV gives four times the power.
Unit prefixes. Convert mA, kΩ and minutes before calculating.
“Current is used up in a bulb.” Energy is transferred; the current in and out is the same.
Using the battery’s emf for one element when it is not the only element in the loop.
Trusting the rating in every circuit. A 12 W bulb can be dimmer than a 3 W bulb.

A motor carries 0.50 A with 12 V across it. What is its power? (6.0 W)
The ΔV across a resistor doubles. What happens to its power? (× 4)
How much energy does a 60 W lamp transfer in 5.0 minutes? (1.8 × 10⁴ J)
Two bulbs share one loop. Which is brighter: the one with larger or smaller R? (Larger R)