# How emf is induced in single phase system ? single phase generation .

## EMF induced in single phase system

We know that an alternating emf can be generated either by rotating a coil within a stationary magnetic field, as illustrated in fig.(a) or by rotating a magnetic field within a stationary coil, as illustrated in fig.(b). The emf generated, in either case, will be of sinusoidal waveform. The magnitude of emf generated in the coil depends upon the number of turns on the coil, the strength of magnetic field and the speed at which the coil or magnetic field rotates. The former method is employed in case of small ( single phase generation ) ac generators while the later one is employed for large sized ac generators.

Now, consider a rectangular coil of N turns rotating in counter-clockwise direction with angular velocity of  radians per second in a uniform magnetic field, as illustrated in fig. (c).

Let, the time be measured from the instant of coincidence of the plane of the coil with the X-axis. At this instant maximum flux,

links with the coil. Let the coil assume the position, as shown in figure, after moving in counter-clockwise direction for t seconds.

In this position, the component of flux perpendicular to the plane of coil =

Hence, flux linkages of the coil at this instant — Number of turns on coil x linking flux

i.e. instantaneous flux linkages

Since, emf induced in a coil is equal to the rate of change of flux linkages with minus sign. EMF induced at any instant,

So, the emf induced varies as the sine function of the time angle wt, and if emf induced is plotted against time, a curve of sine wave shape is obtained as illustrated in figure (d). Such an emf is called the sinusoidal emf The sine curve is completed when the coil rotates through an angle of 2 pie radians. The induced emf e will have maximum value, represented by Emax , when the coil has turned through pie/2 radians (or 900 ) in counter- clockwise direction from the reference axis (i.e. 0X axis).