**Power** is the rate at which work is done, or the derivative of work with respect to time. The SI unit is the watt (W, equal to J/s). The formula for power is

- $ P_\mathrm{avg} = \frac{\Delta W}{\Delta t}\, $
- $ P = \lim _{\Delta t\rightarrow 0} \frac{\Delta W}{\Delta t} = \frac{\mathrm{d}W}{\mathrm{d}t}\, $

One can easily see that this is the same as the dot product of force and velocity. In rotational systems, power is equal to the dot product of torque (`τ`) and angular velocity (`ω`, measured in radians per second),

- $ P(t) = \tau \cdot \omega $

As the derivative of work, power comes in many forms. In the case of an electric circuit, power is equal to

- $ P = IV = I^2 R = \frac{V^2}{R} $

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