Inductance calculation from physical dimension of coil

A general formula for the inductance of a coil can be found by using an equivalent Ohm’s law for magnetic circuit and the formula for reluctance. Consider a solenoid-type electromagnet/toroid with a length much greater than its diameter (at least the length is ten times as great as its diameter). This will produce a uniform magnetic field inside the toroid. The length ‘l’of a toroid is the distance around the centre axis of its core , as indicated in fig by dotted line. Its area ‘ A ’ is the cross-sectional area of the toroid, also indicated in that figure.

A toroidal inductor

Appling ampere-circuital law for magnetic circuit one can write the following relation

We know, flux is always given by the product of flux density ( B ) and area ( A ) through which flux density ids uniform. That is,

where B = μ H and H is the uniform field intensity around the mean magnetic path length ‘l’. Substituting the equation into the defining equation for inductance, equation gives

Continuity condition of Inductors

The current that flows through a linear inductor must always be a continuous. From the expression, the voltage across the inductor is not proportional to the current flowing through it but to the rate of change of the current with respect to time, . The voltage across the inductor  is zero when the current flowing through an inductor does not change with time. This observation implies that the inductor acts as a short circuit under steady state dc current. In other words, under the steady state condition, the inductor terminals are shorted through a conducting wire. Alternating current (ac), on the other hand, is constantly changing; therefore, an inductor will create an opposition voltage polarity that tends to limit the changing current. If current changes very rapidly with time, then inductor causes a large opposition voltage across its terminals. If current changes through the inductor from one level to another level instantaneously i.e. in dt = 0 sec., then the voltage across it would become infinite and this would require infinite power at the terminals of the inductor. Thus, instantaneous changes in the current through an inductor are not possible at all in practice.