Electrical Power

Electrical power tells us how quickly electrical energy is transferred. Think of it like the “speed” of delivering energy. A powerful kettle heats water faster because it transfers more energy each second.

Key ideas and equations

• Definition: Power is the rate of energy transfer: $P = \dfrac{E}{t}$
• Units: Power in watts (W), energy in joules (J), time in seconds (s). $1\,\text{W} = 1\,\text{J s}^{-1}$.
• From circuits: $P = IV$ (current × voltage)
• Using $V=IR$: $P = I^2 R$ and $P = \dfrac{V^2}{R}$
• Energy used over time: $E = Pt$ and $E = IVt$
• Large appliances use kilowatts: $1\,\text{kW} = 1000\,\text{W}$
• Billing unit: kilowatt-hour (kWh). $1\,\text{kWh} = 3.6 \times 10^6\,\text{J}$

Understanding the terms

• Voltage (V): energy shifted per coulomb of charge. Higher voltage can push more energy per charge.
• Current (I): rate of flow of charge. More charge per second means more energy moved each second.
• Resistance (R): how much a component opposes current.

Common misconceptions

• “High voltage means high power.” Not always. Power depends on both $I$ and $V$: $P=IV$.
• “kWh is a power.” It is energy used; bills charge per kWh.