Inductor and Switch

Given below is Inductor with Voltage Pulse

Graph of Voltage Pulse is given below

To solve the issue of linearly increasing current in the circuit due to constant voltage source we have introduced a switch which is closed for a short period of time to provide a voltage pulse. A voltage pulse having amplitude 1V and width of 1 ms is provided to an inductor having inductance 1 mH. There are three cases for which we have to find the current flowing in the circuit, which are before closing the switch, after closing switch and during opening the switch.

Before switch is closed

Before the switch is closed, the circuit is not completed and no current flows through the inductor. Also there is no magnetic field existing across the inductor. Hence I₀ = 0.

[Tex]I = \frac{1}{L}\int_{-E}^{0}Vdt+I_{0}\\ \hspace{1mm}\\ I = \frac{1}{10^{-3}}\int_{-E}^{0}0dt + 0\\ \hspace{1mm}\\ I = 10^{3}[0]_{-E}^{0}\\ \hspace{1mm}\\ I = 10^{3}[(0\times0)-(0\times-E)]\\ \hspace{1mm}\\[/Tex]

∴ I = 0 A for any value of E

After switch is closed

At t = 0, the switch is closed for 1 ms making a closed circuit for this particular duration. The current in the circuit steadilty increases according the formula,

[Tex]I = \frac{1}{L}\int_{0}^{T}Vdt+I_{0}\\ \hspace{1mm}\\ I = \frac{1}{10^{-3}}\int_{0}^{10^{-3}}1dt+0\\ \hspace{1mm}\\ I = 10^3[t]_{0}^{10^{-3}}\\ \hspace{1mm}\\ I = 10^3[10^{-3}-0]\\[/Tex]

∴ I = 1 A

After 1 ms the switch is opened stopping the current flow to the inductor.

During switch is opened

A problem arises during the opening of the switch. Theoretically if we try to find voltage across the inductor during this period, it comes to infinity since the current abruptly changes from 1 A to 0 A due to opening of the circuit. However practically the current takes some time let us consider it as 1 μs. To find the practical voltage across the inductor,

[Tex]V = L\frac{dI}{dt}\\ \hspace{1mm}\\ V = 10^{-3}[\frac{0-1}{10^{-6}}]\\ \hspace{1mm}\\ V = -\frac{1}{10^{-3}}\\ \hspace{1mm}\\ V = -10^3[/Tex]

∴ V = -1 kV

Such high voltages cause arcs and electric current starts to travel through air. This process only stops after the inductor does not have any current stored in the form of magnetic field. These arcs are dangerous and can be avoided by connecting a diode which acts as a safe path to discharge the inductor. A diode is a semiconductor device which allows the current to flow in only one direction. In the below circuit diagram, the diode conducts while the switch is being opened and discharges the inductor. When the switch is closed, no current flows through the diode.

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.