UNIT-II
Alternating Quantities:
Introduction, Generation of AC Voltages, Root Mean Square and Average Value of
Alternating Currents and Voltages, Form Factor and Peak Factor, Phasor Representation
of Alternating Quantities, Single Phase RLC Circuits, Introduction to 3-Phase AC
System.
Generation of Alternating Voltages
and Currents
Alternating voltage may be generated
by rotating a coil in a magnetic field, as shown in Figure (a) or by rotating a magnetic field within a stationary coil, as shown in
Figure(b).
The value of the voltage generated
depends, in each case, upon the number of turns in the coil, strength of the
field and the speed at which the coil or magnetic field rotates. Alternating
voltage may be generated in either of the two ways shown above, but
rotating-field method is the one which is mostly used in practice.
Equations of the Alternating Voltages
and Currents
Consider a rectangular coil, having N turns and rotating
in a uniform magnetic field, with an angular velocity of ω radian/second, as shown in Figure. Let time be measured from the X-axis. Maximum flux
ϕm is linked with the coil, when its
plane coincides with the X-axis. In time t seconds, this coil
rotates through an angle θ = ωt. In this deflected position, the component of
the flux which is perpendicular to the plane of the coil, is ϕ = ϕm cos ω t. Hence, flux linkages of the coil at any time are Nϕ = Nϕm cos ω t
According to Faraday’s Laws of
Electromagnetic Induction, the e.m.f. induced in the coil is given by the rate
of change of flux-linkages of the
coil. Hence, the value of the induced e.m.f. at this instant (i.e. when θ = ωt) or the
instantaneous value of the induced e.m.f. is
When the coil has turned through 90º i.e. when θ = 90º, then sin θ= 1, hence e has maximum value,
say Em. Therefore, from Equation we get
where Bm = maximum flux density in Wb/m2 ; A = area of the coil in m2
f = frequency of rotation of the coil in rev/second
Substituting this value of Em in Equation we get
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