Understanding Power in Physics

Power is the rate at which work is done or energy is transferred. It measures how quickly energy is converted from one form to another. The SI unit of power is the Watt (W), equal to one Joule per second.

Basic Power Formula

The fundamental formula for power is P = W / t, where P is power, W is work or energy, and t is time. This applies to any situation where energy is transferred.

Electrical Power

In electrical circuits, power can be calculated using several equivalent formulas:

• P = V × I - Voltage times Current
• P = I² × R - Current squared times Resistance
• P = V² / R - Voltage squared divided by Resistance

These formulas are derived from Ohm's Law (V = IR) and are useful in different situations depending on which quantities are known.

Mechanical Power

For mechanical systems, power can be calculated as:

• P = F × v - Force times velocity (linear motion)
• P = τ × ω - Torque times angular velocity (rotational motion)

Power Units

• Watt (W): SI unit, 1 W = 1 J/s
• Kilowatt (kW): 1 kW = 1000 W
• Megawatt (MW): 1 MW = 1,000,000 W
• Horsepower (hp): 1 hp = 745.7 W

Common Applications

• Rating electrical appliances and devices
• Calculating electricity costs
• Engine and motor specifications
• Solar panel output
• HVAC system sizing

Power vs Energy

Power and energy are related but different concepts. Energy is the capacity to do work, while power is the rate of energy transfer. Your electricity bill charges for energy used (kWh), which is power multiplied by time.

Worked Example: Sizing a Kettle Circuit

A kettle drawing 10 A on a 230 V supply consumes P = V × I = 230 × 10 = 2,300 W (2.3 kW). If it runs for 3 minutes (0.05 h), it uses 2.3 × 0.05 = 0.115 kWh of energy. The same tool works in reverse: a 1,500 W space heater on a 120 V US circuit draws I = P / V = 12.5 A — close to the 15 A breaker limit, which is why two heaters on one circuit trip it.