Relation Between Current and Voltage
Below steps can be followed to derive the relation between current flowing through an inductor and voltage across it. Magnetic flux present across the inductor is equal to it’s inductance times current flowing through it.
Mathematically, it can be written as:
[Tex]\Phi = LI[/Tex]
Also induced voltage across the inductor is equal to the rate of change of magnetic flux per unit time.
[Tex]V = \frac{d\Phi}{dt}[/Tex]
Substituting the value of Φ in above equation we get,
[Tex]V = \frac{dLI}{dt}\\ \hspace{1mm}\\ \therefore V = L\frac{dI}{dt}[/Tex]
The above equation describes the relation between voltage and current respectively. The above equation can be easily rearranged to find current if we know voltage and inductance beforehand.
[Tex]\frac{V}{L} = \frac{dI}{dt}\\ \hspace{1mm}\\[/Tex]
Integrating both sides with respect to time,
[Tex]I = \int \frac{V}{L}dt\\ \hspace{1mm}\\ \therefore I = \frac{1}{L}\int Vdt[/Tex]\
Inductor I-V Equation in Action
The inductor is a passive element that is used in electronic circuits to store energy in the form of magnetic fields. It is usually a thin wire coiled up of several turns around a ferromagnetic material. Inductors are used in transformers, oscillators, filters, etc. The amount of energy that can be stored by the inductor in the form of the magnetic field is called inductance measured in Henry named after the famous scientist Joseph Henry.
Inductor works on the principle of one of Maxwell’s four equations which states that a changing electric field produces a changing magnetic field and vice versa. Unlike a capacitor, an inductor cannot sustain the stored energy as soon as the external power supply is disconnected because the magnetic field decreases steadily as it is responsible for current flow in that circuit in the absence of the power supply.
Table of Content
- Inductor I-V Equations
- Relation Between Current and Voltage
- Inductor Voltage is Proportional To The Rate of Change of Current
- Inductor and Current Source
- Inductor and Voltage source
- Inductor and Switch
- Solved Examples