Power (Physics)

Power is defined at the rate at which Work is done.

• The SI unit for power is the watt (W), defined as 1 W = 1 J/S

Mathematically, the average power over time is $P_{avg}=\frac{\Delta W}{\Delta t}$ More specifically, $P=\frac{dW}{dt}$

Kilowatt hour is the amount of energy consulted in one our at a rate of 1000W.

Electric Power

Also see Horsepower for something more pratical. $p=\frac{dw}{dt}=vi=R{i}^2=\frac{v^2}{R}$

Passive sign convention (PSC) $\to$ Moving from higher potential (+) to lower potential (-)

Absorbed Power $\to$ when direction of current is from positive (+) to negative (-) of the reference voltage. If $p_{abs}>0$, power is actually absorbed. If $p_{abs}<0$, power is actually supplied.

Delivered/Supplied Power $\to$ when direction of current is from negative (-) to positive (+) of the reference voltage.

Note that for every element, $p_{abs}=-p_{sup}$

Power is often measured in Kilowatt-hour (kWh) rather than joules (J) .

Power, Torque and Angular Velocity

Torque (τ) and rotational speed (ω) are inversely proportional due to the relation of $P=\tau \omega$ This comes from a derivation of Rotational Work $P=\frac{dW}{dt}=\frac{d}{dt}(\tau \theta )=\tau \frac{d\theta }{dt}=\tau \omega$

Related

• Work
• AC Power Analysis