## Generation of a Sine Wave of Voltage

*it changes in magnitude from instant to instant as varying values of flux are cut per second*and the other one is

*it changes in direction as coil side change positions under north and south poles*, implies that alternating emf is generated. This means that the voltage is maximum as mentioned in our last topic here when the position of the coil is just like shown in the figure below:

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

be:

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

cycle).

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