The voltage waveform produced as the armature rotatesthrough 360 degrees rotation is called a sine wavebecauseinstantaneous voltage is related to the trigonometric functioncalled sine (sin q = sine of the angle). The sine curve representsa graph of the following equation:

e Epeak = ´sin q

Instantaneous voltage is equal to the peak voltage times thesine of the angle of the generator armature. The sine value isobtained from trigonometric tables. The following table reflectsa few angles and their sine value.

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The following example illustrates instantaneous values at 90,150, and 240 degrees. The peak voltage is equal to 100 volts.By substituting the sine at the instantaneous angle value, theinstantaneous voltage can be calculated.

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Alternating voltage and current are constantly changingvalues. A method of translating the varying values into anequivalent constant value is needed. The effective value ofvoltage and current is the common method of expressing thevalue of AC. This is also known as the RMS (root-meansquare)value. If the voltage in the average home is said to be120 volts, this is the RMS value. The effective value figuresout to be 0.707 times the peak value.

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The effective value of AC is defined in terms of an equivalentheating effect when compared to DC. One RMS ampere ofcurrent flowing through a resistance will produce heat at thesame rate as a DC ampere.For purpose of circuit design, the peak value may also beneeded. For example, insulation must be designed to withstandthe peak value, not just the effective value. It may bethat only the effective value is known. To calculate the peakvalue, multiply the effective value by 1.41. For example, if theeffective value is 100 volts, the peak value is 141 volts.


The circuits studied to this point have been resistive. Resistance and voltage are not the only circuit properties that effect current flow, however. Inductance is the property of an electric circuit that opposes any change in electric current.Resistance opposes current flow, inductance opposes change in current flow. Inductance is designated by the letter "L". The unit of measurement for inductance is the henry (h).


Current flow produces a magnetic field in a conductor. The amount of current determines the strength of the magnetic field. As current flow increases, field strength increases, and as current flow decrease, field strength decreases.

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Any change in current causes a corresponding change in the magnetic field surrounding the conductor. Current is constant in DC, except when the circuit is turned on and off, or when there is a load change. Current is constantly changing in AC,so inductance is a continual factor. A change in the magnetic field surrounding the conductor induces a voltage in the conductor. This self-induced voltage opposes the change in current. This is known as counter emf. This opposition causes a delay in the time it takes current to attain its new steady value. If current increases, inductance tries to hold it down. If current decreases, inductance tries to hold it up. Inductance is somewhat like mechanical inertia, which must be overcome to get a mechanical object moving, or to stop a mechanical object from moving. A vehicle, for example, takes a few moments to accelerate to a desired speed, or decelerate to a stop.


Inductance is usually indicated symbolically on an electricaldrawing by one of two ways. A curled line or a filled rectanglecan be used.

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Inductors are coils of wire. They may be wrapped around a core. The inductance of a coil is determined by the number of turns in the coil, the spacing between the turns, the coil diameter, the core material, the number of layers of windings,the type of winding, and the shape of the coil. Examples of inductors are transformers, chokes, and motors.


In a resistive circuit, current change is considered instantaneous.If an inductor is used, the current does not change asquickly. In the following circuit, initially the switch is openand there is no current flow. When the switch is closed,current will rise rapidly at first, then more slowly as the maximumvalue is approached. For the purpose of explanation, aDC circuit is used.

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The time required for the current to rise to its maximum value is determined by the ratio of inductance, in henrys, to resistance, in ohms. This ratio is called the time constant of the inductive circuit. A time constant is the time, in seconds,required for the circuit current to rise to 63.2% of its maximum value. When the switch is closed in the previous circuit,current will begin to flow. During the first time constant current rises to 63.2% of its maximum value. During thesecond time constant, current rises to 63.2% of the remaining 36.8%, or a total of 86.4%. It takes about five time constants for current to reach its maximum value.

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Similarly, when the switch is opened, it will take five timeconstants for current to reach zero. It can be seen that inductanceis an important factor in AC circuits. If the frequency is60 hertz, current will rise and fall from its peak value to zero120 times a second.

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