and will diminish to zero as the coil rotates clockwise toward the position as shown below:
Then, as the coil continues to rotate clockwise, the polarities will
change. Assuming uniform flux distribution between north and south
poles, the generated voltage in a coil located from the vertical will
e = Em sin α
Consider the figure below for us to analyze why this relationship mentioned above happened.
It was come up to the relationship between instantaneous voltage e and maximum voltage Em is that a coil side such as a,
moving tangentially to a circle as indicated, cut lines of force in
proportion to its vertical component of the motion. If the vector length
ay in the figure above represents a constant rotating velocity, it should be obvious that vector xy is, its vertical component; the vector length ax is
the horizontal component and it emphasize that motion in this direction
involves no flux- cutting action. Since the velocity ratio xy/ay=sinα
is also a measure of the voltage in coil side a with respect to
the maximum voltage (when the coil is located horizontally) it follows
that sinα is a varying proportionality factor that equates e to Em.
The equation above may be used to determine a succession of generated
voltage values in a coil as it rotates through a complete revolution.
This is just by computing with its selected angular displacements.
A more convenient way of representing the instantaneous voltage equation
mentioned above is to draw a graph to illustrate a smooth variation of
voltage with respect to the angular position of the coil, this graph is
called a sine wave. The wave repeats itself and it is called a periodic, then each complete succession of values is called a cycle, while each positive or negative half of the cycle is called alternation.
Now, we can say that an alternating voltage as an emf that varies in
magnitude and direction periodically. Then, when the emfs are
proportional to the trigonometric sine function, it is referred to a sinusoidal alternating voltage. However, there are also some periodic waves which do not follow this shape and they are called non sinusoidal waves. This topic will be covered when we reached more complicated analysis is AC Circuits.
Lets have a practical example of a problem using the equation above just for you to appreciate the presented formula above:
Problem : The voltage in an ac circuit varies harmonically with time
with a maximum of 170V. What is the instantaneous voltage when it has
reached 45 degree in its cycle?
Using, e = Em sin α = 170V x sin (45 degree) = 170V x 0.71 = 120 V.
In the common 60 cycle ac circuit, there are 60 complete cycle each
second; i.e. the time interval of 1 cycle is 1/60 sec. It should be
noted that this corresponds to a reversal in a direction of the current
every 1/120 sec. (since the direction reverses twice during each