Inductance Equation

Inductance Equation:

Inductance Equation – A wire of certain length, when twisted into a coil becomes a basic inductor. If current is made to pass through an inductor, an electromagnetic field is formed. A change in the magnitude of the current changes the electromagnetic field. Increase in current expands the fields, and decrease in current reduces it. Therefore, a change in current produces change in the electromagnetic field, which induces a voltage across the coil according to Faraday’s law of electromagnetic induction.

The unit of inductance is henry, denoted by H. By definition, the inductance is one henry when current through the coil, changing at the rate of one ampere per second, induces one volt across the coil. The symbol for inductance is shown in Fig. 1.4.

Inductance Equation

The current-voltage relation is given by ,

Inductance Equation

 

where v is the voltage across inductor in volts, and i is the current through inductor in amps. We can rewrite the above equations as

Inductance Equation

Integrating both sides, we get

Inductance Equation

From the above equation we note that the current in an inductor is dependent upon the integral of the voltage across its terminals and the initial current in the coil, i(0).

The power absorbed by inductor is

Inductance EquationThe energy stored by the inductor is

Inductance Equation

From the above discussion, we can conclude the following.

  1. The induced voltage across an inductor is zero if the current through it is constant. That means an inductor acts as short circuit to dc.
  1. A small change in current within zeto time through an inductor gives an infinite voltage across the inductor, which is physically impossible. In a fixed inductor the current cannot change abruptly.
  1. The inductor can store finite amount of energy, even if the voltage across the inductor is zero, and
  2. A pure inductor never dissipates energy, only stores it. That is why it is also called a non-dissipative passive element. However, physical inductors dissipate power due to internal resistance.