Self-inductance is the ration between the induced electromotive force (EMF) across a coil to the rate of change of current through this coil. Self-inductance is related term to self induction phenomenon because self-induction generates self-inductance. We denote self-inductance or Co-efficient of with English letter L. Its unit is Henry (H). First, we have to know what self-induction is. Self-induction is the phenomenon by which in a coil, the change in electric current produces an induced electromotive force across this coil itself. This induced electromotive force (E) across this coil is proportional to the current changing rate. The higher the rate of change in current causes higher value of emf.
We can write that, But the actual equation is
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Why there is Minus (-) sign? According to Lenz’s Law, this induced emf across this coil is always opposite to the direction of the rate of change of current. When the current (i) flows through a coil some electric flux produces inside the coil. At that moment of self-induction phenomenon, the induced emf generates to oppose this rate of change of current in that coil. So their values are same but sign differs.
Video Presentation of Self InductanceFor the DC source, when the switch is ON, i.e. just at t = 0+, a current will flow from its zero value to a certain value and with respect to time there will be a rate of change in current momentarily. This current produces changing magnetic flux lines (φ) through this coil. As current changes its value to zero to a certain value that is why magnetic flux (φ) gets rate of change with respect to the time. Now apply Faraday's Law of Electromagnetic Induction in this coil, Where, N is the number of turn of the coil and e is the induced EMF across this coil. Lenz's law states that an induced current due to induced EMF has a direction such that its magnetic field opposes the change in magnetic field that induced the current. As per Lenz’s law we can write down this equation of induced voltage across the coil, Now, we can modify this equation to calculate the value of inductance of a coil. So,[B is the flux density i.e. B =φ/A, A is area of the coil], [Nφ or Li is called magnetic flux Linkage and it is denoted by Ѱ] Where H is the magnetizing force due to which magnetic flux lines flow from south to north pole inside the coil, l (small L) is the effective length of the coil and r is the radius of the coil cross-sectional area. Self inductance, L is a geometric quantity; it depends only on the dimensions of the solenoid, and the number of turns in the solenoid. Furthermore, in a DC circuit when the switch is just closed, then only momentarily effect of self-inductance occurs in the coil. After then no effect of self inductance is in the coil. It is because of a steady flow of unidirectional current through this coil after certain time.
But in AC circuit, the alternating effect of current always causes the self-induction in the coil, and a certain value of this self-inductance gives the inductive reactance (XL = 2πfL) depending on the value of supply frequency.
In the electrical circuit the coils those are used known as inductor having inductance values of L1, L2, L3 etc. and when they are series combined then equivalent inductance of them is calculated as When they are in parallel, then