Electrical Energy and Electrical Power
Simple Explanation
Electrical power (P=VI=IΒ²R=VΒ²/R) measures how fast electrical energy is being converted into another form (heat, light, motion); the total energy used over a period of time is simply E=Pt.
Why Do We Need It?
These formulas are the basis for everything from reading an appliance's wattage rating to calculating an electricity bill β power tells you the RATE of energy use, and multiplying by time gives the TOTAL energy consumed.
Formula
Electrical Power and Energy
P = VI = IΒ²R = VΒ²/R; E = Pt
Electrical power is the rate at which electrical energy is converted (to heat, light, motion, etc.); the total energy used over a time interval is simply power multiplied by time.
- P
- β electrical power, in watts (W)
- V
- β voltage across the component, in volts (V)
- I
- β current through the component, in amperes (A)
- R
- β resistance of the component, in ohms (Ξ©)
- E
- β total electrical energy used, in joules (J)
- t
- β time, in seconds (s)
When to use it: Whenever the electrical power delivered to a component, or the total energy used over some time, needs to be found.
Worked Example
Find electrical power and total energy used
A device operates at 12 V, drawing 3 A of current, for 10 seconds. Find its power and the total energy it uses.
Why Does This Work?
Voltage is energy transferred per unit charge, and current is charge flowing per unit time β multiplying them together gives energy transferred per unit time, which is exactly the definition of power; multiplying power by the duration it acts then recovers the total energy transferred.
Real-Life Example
Reading a household electricity bill
An electricity bill charges based on the total kilowatt-hours (kWh) of energy used β a unit that is exactly power (in kW) multiplied by time (in hours).
A 1000 W appliance running for 2 hours uses exactly 1 kW Γ 2 h = 2 kWh of energy β the same E=Pt relationship this formula describes, just in everyday billing units.
Practice
A device operates at 6 V, drawing 4 A, for 20 seconds. Find the total energy it uses, in J.
MediumCommon mistake
Confusing power (the RATE of energy use, in watts) with energy (the TOTAL amount used, in joules or kilowatt-hours) β a device can have high power but use little total energy if it only runs briefly.
Quick Review
- P = VI = IΒ²R = VΒ²/R.
- E = Pt β total energy is power times time.
- Power is a rate; energy is a total amount.