4.6:
Energy Stored in Inductors
An inductor is designed to store energy in its magnetic field, which is generated by the current flowing through its coils.
When the current is constant, the voltage across the inductor is zero, causing it to behave as a short circuit for direct current.
The energy stored within an inductor equals the integral of the instantaneous power delivered over time.
By integrating within the limits, an expression for the stored energy consisting of two terms is obtained. The second term is zero, considering the initial condition where no current flowed through the inductor.
Ideal inductors do not dissipate energy, allowing the stored energy to be retrieved later.
However, non-ideal inductors exhibit winding resistance, which originates from the conductor's coils and is presented in series with the inductance.
Although this winding resistance can lead to energy dissipation, it is typically so small that it can be neglected in practical scenarios.
Non-ideal inductors also exhibit winding capacitance attributable to capacitive coupling between the conducting coils. However, this winding capacitance is typically negligible except at high frequencies.
4.6:
Energy Stored in Inductors
An inductor is ingeniously crafted to accumulate energy within its magnetic field. This field is a direct result of the current that meanders through its coiled structure. When this current maintains a steady state, there is no detectable voltage across the inductor, prompting it to mimic the behavior of a short circuit when faced with direct current.
In terms of gauging the energy stored within an inductor, it is equivalent to the integral of the power delivered at every individual moment, all accumulated over a specific duration of time. Mathematically, energy stored in an inductor is expressed as
Where w is the energy stored in the inductor, L is the inductance and i is the current passing through the inductor.
Ideal inductors have a noteworthy characteristic – they do not dissipate energy. This trait allows the energy stored within them to be harnessed at a later point in time. However, this ideal scenario is slightly marred when dealing with non-ideal inductors.
Non-ideal inductors exhibit a phenomenon known as winding resistance. This resistance stems from the coils of the conductor and presents itself in series with the inductance. While this winding resistance has the potential to contribute to energy dissipation, it is typically so minuscule that it can be conveniently overlooked in practical applications.
Additionally, non-ideal inductors also display winding capacitance. This is due to the capacitive coupling that occurs between the conducting coils. However, this winding capacitance is usually so minute that it can be disregarded, except when dealing with high frequencies.