To magnetise the magnetic circuits of electrical devices such as transformers, AC machines, electromagnetic relays, etc., AC supply is used.

The magnetisation of magnetic circuits is called their excitation.

The magnetic circuits are never excited by DC supply, because in case of DC excitation the steady-state current is determined by the impressed voltage and resistance of the circuit.

\(L_{coil}\) comes into picture only during transient period i.e., when the current is building-up or decaying during switching (ON or OFF) instants.

\(\phi\) adjusts itself in accordance with \(I_{\text{steady-state}}\) so that the relationship imposed by magnetisation (B-H) curve in satisfied.

However, with AC excitation, inductance comes into picture even at steady-state condition.

As a result for most of the magnetic circuits (not for all) the flux is determined by the impressed voltage and frequency.

Then the magnetisation current adjusts itself in accordance with this flux so that the relationship imposed by the magnetisation (B-H) curve is satisfied

Usually, for economic reasons, the normal working \(B\) is kept beyond the linear portion of the magnetisation curve thus accurate analysis cannot be predicted for determining self inductance.

However, for all practical purposes the parameters of the magnetic circuit are considered to be constant.

\[\begin{aligned} e&=N \frac{d \phi}{d t} \\ \phi&=\phi_{m} \sin \omega t=\phi_{m} \sin 2 \pi f t \quad \ldots(i) \\ e&=N \frac{d \phi}{d t}=N \frac{d}{d t}\left(\phi_{m} \sin 2 \pi f t\right) \\ &=2 \pi f N \phi_{m} \cos 2 \pi f t=2 \pi f N \phi_{m} \sin \left(2 \pi f t+\frac{\pi}{2}\right) \ldots(i i) \\ E_{m}&=2 \pi f N \phi_{m} \\ E_{r m s}&=\frac{E_{m}}{\sqrt{2}}=\frac{2 \pi f N \phi_{m}}{\sqrt{2}}=4 \cdot 44 f N \phi_{m} \end{aligned}\]

Eqs. (i) and (ii) reveal that the induced emf leads the flux and hence the exciting current by \(\frac{\pi}{2}\) radian or \(90^{\circ} .\)

Induced emf & coil resistance drop oppose the applied \(V\).

In electrical machines, usually the drop in \(R\) is only a few percent of \(V\) and therefore, neglected

\(E\) and \(V\) may be considered equal in magnitude.