Energy stored by Inductors and Capacitors

Energy stored by Inductors and Capacitors

Energy is not dissipated but stored in reactive elements capacitor and inductor. It depends on the steady state condition. Final voltage across the capacitor and final current established in an inductor. Energy stored by Inductors and Capacitors explained below,

Energy stored by Capacitor

A capacitor (formerly known as condenser) is a passive two-terminal electrical component used to store energy in an electric field.

The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric (insulator); for example, one common construction consists of metal foils separated by a thin layer of insulating film. Capacitors are widely used as parts of electrical circuits in many common electrical devices.

When there is a potential difference (voltage) across the conductors, a static electric field develops across the dielectric, causing positive charge to collect on one plate and negative charge on the other plate.

Energy is stored in the electrostatic field. An ideal capacitor is characterized by a single constant value, capacitance, measured in farads. This is the ratio of the electric charge on each conductor to the potential difference between them.

The capacitance is greatest when there is a narrow separation between large areas of conductor, hence capacitor conductors are often called “plates,” referring to an early means of construction.

In SI units, a capacitance of one farad means that one coulomb of charge on each conductor causes a voltage of one volt across the device.

An ideal capacitor is wholly characterized by a constant capacitance C, defined as the ratio of charge ±Q on each conductor to the voltage V between them

C = Q / V

Energy storage

W = 0.5 * Q^2 / C = 0.5 * C * V^2 = 0.5 * V * Q

Work must be done by an external influence to “move” charge between the conductors in a capacitor.

When the external influence is removed the charge separation persists in the electric field and energy is stored to be released when the charge is allowed to return to its equilibrium position. The work done in establishing the electric field, and hence the amount of energy stored, is given by

Energy stored by Inductor

Inductance (L) results from the magnetic field forming around a current-carrying conductor which tends to resist changes in the current. Electric current through the conductor creates a magnetic flux proportional to the current.

A change in this current creates a corresponding change in magnetic flux which, in turn, by Faraday’s Law generates an electromotive force (EMF) that opposes this change in current.

Inductance is a measure of the amount of EMF generated per unit change in current. For example, an inductor with an inductance of 1 henry produces an EMF of 1 volt when the current through the inductor changes at the rate of 1 ampere per second. The number of loops, the size of each loop, and the material it is wrapped around all affect the inductance.

Stored energy

Estored = 0.5 * L * I^2

where L is inductance and I is the current through the inductor.
This relationship is only valid for linear (non-saturated) regions of the magnetic flux linkage and current relationship.

The energy (measured in joules, in SI) stored by an inductor is equal to the amount of work required to establish the current through the inductor, and therefore the magnetic field.