# 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}=ΔtΔW $ More specifically, $P=dtdW $

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=dtdw =vi=Ri_{2}=Rv_{2} $

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

**Absorbed Power** $→$ 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** $→$ 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 $P=τω$ This comes from a derivation of Rotational Work $P=dtdW =dtd (τθ)=τdtdθ =τω$