AC Voltage Applied To Inductor

By Kunal Kapoor

In case of a DC circuit, an inductor acts as a closed connection offering no resistance to current. But in AC currents, an inductor’s voltage drop equation is:

A simple inductor connected to an AC power source:


Voltage across the source be , Vm is Max voltage

As per Kirchhoff’s loop rule, voltage equation is: 

Where L is the inductance of the inductor and  is self-induced Faraday emf in the inductor. Negative sign follows from Lenz’s law.

Equation now becomes : 

To obtain the current, we integrate di/dt with respect to time:and get

The source has an emf which oscillates symmetrically about zero, the current it sustains also oscillates symmetrically about zero, so that no constant or time-independent component of the current exists. Therefore, the integration constant is zero.

Thus equation becomes , Where im is and Xl = ω L

amplitude of the current is,. Dimension of inductive reactance is the same as that of resistance and its SI unit is ohm 



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