Electric Power and Energy
A 3D bench of appliances that actually behave: a lamp whose filament glows, a heater whose bars go red, a motor that spins. Read the rating plate, work out R = V²/P, and watch all three power formulae agree — until you select the motor, where V is not IR and V²/R falls apart.
How to use this simulation
- Pick the 60 W lamp, 150 W lamp or 2000 W heater and read the rating plate
- Drag the supply slider to run each appliance above or below its rated voltage
- Press Start the clock to accumulate energy and watch the joules add up
- Select the 40 W motor and compare all three power formulae against each other
What to look for
- For the lamp and the heater, P = VI, P = I²R and P = V²/R all give the same number
- Running an appliance below its rated voltage drops the power faster than the voltage
- The 2000 W heater draws far more current at the same supply than either lamp
- For the motor only P = VI survives — the other two disagree because V ≠ IR
- Energy is power multiplied by time, so a small appliance left on can beat a large one switched on briefly
The physics behind it
Electrical power is P = VI in every case, because it follows directly from energy per unit charge times charge per unit time. The familiar variants P = I²R and P = V²/R are obtained by substituting Ohm's law, so they only hold where V = IR does — that is, for a purely resistive device such as a lamp or a heater. A motor converts most of its input to mechanical work and generates a back EMF, so its terminal voltage is not IR and the substituted forms give the wrong answer. Energy follows as E = Pt.