# Displacement Power

on . Posted in Classical Mechanics

Displacement power, abbreviated as P or $$P_d$$, also called reactive power, is used in electrical engineering and power systems.  It represents the portion of electrical power that does not perform useful work in an electrical circuit but is necessary for the proper operation of devices like motors and transformers.  Displacement power is associated with the phase difference between voltage and current in an alternating current circuit.

In a circuit with inductive or capacitive elements, there is a phase difference between voltage and current due to the reactive nature of these components.  In such cases, displacement power represents the portion of power that contributes to maintaining the electromagnetic fields in these elements but does not perform useful work.

Utilities and power system operators need to manage both real power and reactive power to ensure the efficient and reliable operation of the electrical grid.  Excessive reactive power can lead to voltage stability issues, while inadequate reactive power can result in voltage sags and other operational problems.  Power factor correction devices, such as capacitors and inductors, are often used to optimize the balance between real power and reactive power in a system.

### Displacement power formula

$$P \;=\; \dfrac{F \cdot t}{ \delta}$$     (Displacement Power)

$$F \;=\; P \; \delta \; t$$

$$\delta \;=\; \dfrac{F \cdot t}{P}$$

$$t \;=\; \dfrac{P \cdot \delta }{ F}$$

Symbol English Metric
$$P$$ = power $$ft-lbf \;/\; sec$$ $$J \;/\; s$$
$$F$$ = force $$lbf$$ $$N$$
$$\delta$$  (Greek symbol delta) = displacement $$ft$$ $$m$$
$$t$$ = time $$sec$$ $$s$$