Basic Power Formula:

Power = Work ÷ Time

Power from Work:

P = \(\frac{W}{t}\)

• P = Power (Watts, W)
• W = Work (Joules, J)
• t = Time (seconds, s)

Power from Energy:

P = \(\frac{E}{t}\)

• P = Power (Watts, W)
• E = Energy (Joules, J)
• t = Time (seconds, s)

Force and Velocity:

P = F · v

• P = Power (Watts, W)
• F = Force (Newtons, N)
• v = Velocity (meters per second, m/s)

Torque and Angular Velocity:

P = τ · ω

• P = Power (Watts, W)
• τ = Torque (Newton-meters, N·m)
• ω = Angular velocity (radians per second, rad/s)

Basic Electrical Power:

P = V · I

• P = Power (Watts, W)
• V = Voltage (Volts, V)
• I = Current (Amperes, A)

Power in Resistive Circuits:

P = I² · R

P = \(\frac{V²}{R}\)

• R = Resistance (Ohms, Ω)

Fluid Power:

P = \(Δp\) · Q

• P = Power (Watts, W)
• Δp = Pressure difference (Pascal, Pa)
• Q = Flow rate (cubic meters per second, m³/s)

Thermodynamic Power:

P = \(\frac{ΔQ}{Δt}\)

• P = Power (Watts, W)
• ΔQ = Heat energy transferred (Joules, J)
• Δt = Time interval (seconds, s)

Elementary: A student lifts a 5 N book 2 meters in 4 seconds. What power does the student use?

Solution:

• Work = Force × Distance = 5 N × 2 m = 10 J
• Power = Work ÷ Time = 10 J ÷ 4 s = 2.5 W

Middle School: How much energy is used by a 60 W light bulb in 2 hours?

Solution:

• Time in seconds = 2 hours × 3600 s/hr = 7200 s
• Energy = Power × Time = 60 W × 7200 s = 432,000 J = 432 kJ

High School: A motor draws 3 A of current at 120 V. What is its power consumption?

Solution:

• Power = Voltage × Current = 120 V × 3 A = 360 W