Electrical Power and Energy

Electrical Power ($P$) is the rate at which electrical energy is converted into another form of energy. In a circuit, power is determined by the product of the potential difference ($V$) and the current ($I$). The standard unit for power is the Watt ($W$), where $1 W = 1 J/s$. By integrating Ohm’s Law ($V=IR$), we can derive two other vital formulas for power: $P = I^2R$ (useful when current is constant) and $P = \frac{V^2}{R}$ (useful when voltage is constant, such as in parallel home circuits).

While power tells us how 'fast' a device uses energy, Electrical Energy ($E$) tells us the total amount used over time ($t$). The relationship is $E = P \times t$. In physics labs, we use Joules ($J$), but utility companies use the kilowatt-hour ($kWh$) because Joules are too small for billing. One $kWh$ is the energy used by a $1000W$ appliance running for one hour. To convert, remember: $1 kWh = 3.6 \times 10^6 J$.

In the real world, no device is $100\%$ efficient. When a motor runs, some electrical energy is converted into useful kinetic energy, but some is 'wasted' as heat due to resistance and friction. Efficiency is the ratio of useful energy output to total energy input, expressed as a percentage: $Efficiency = \frac{E_{useful}}{E_{total}} \times 100\%$. High-efficiency appliances save money and reduce environmental impact by minimizing this wasted heat.