Electric Power

Power is the rate at which electrical energy is consumed.

$$P = VI = I^2R = \frac{V^2}{R}$$

The SI unit of power is the watt ($\text{W}$).

The commercial unit of electrical energy is the kilowatt-hour ($\text{kWh}$):

$$1\,\text{kWh} = 3.6 \times 10^6\,\text{J}$$

Example

An electric heater of resistance $20\,\Omega$ draws $5\,\text{A}$ of current. Find the power and the heat produced in $30\,\text{s}$.

$$P = I^2 R = (5)^2 \times 20 = 500\,\text{W}$$ $$H = Pt = 500 \times 30 = 15000\,\text{J} = 15\,\text{kJ}$$