VOLTAGE AND CURRENT RELATION AND RMS VALUE OF SINUSOIDThe term RMS stands for Root-Mean-Squared. Mostbooksdefine this as the amount of AC power that produces the same heating effect as an equivalent DC power, or something similar along these lines, but an RMS value is more than just that. The RMS value is the square root of the mean (average) value of the squared function of the instantaneous values. The symbols used for defining an RMS value areVRMSorIRMS.The term RMS, ONLY refers to time-varying sinusoidal voltages, currents or complex waveforms were the magnitude of the waveform changes over time and is not used in DC circuit analysis or calculations were the magnitude is always constant. When used to compare the equivalent RMS voltage value of an alternating sinusoidal waveform that supplies the same electrical power to a given load as an equivalent DC circuit, the RMS value is called the effective value and is generally presented as:VefforIeff.In other words, the effective value is an equivalent DC value which tells you how many volts or amps of DC that a time-varying sinusoidal waveform is equal to in terms of its ability to produce the same power. For example, the domestic mains supply in theUnitedKingdom is 240Vac. This value is assumed to indicate an effective value of 240 Volts RMS. This means then that the sinusoidal RMS voltage from the wall sockets of a UK home is capable of producing the same average positive power as 240 volts of steady DC voltage as shown below.RMS Voltage Equivalent

So how do we calculated theRMS Voltageof a sinusoidal waveform. The RMS voltage of a sinusoid or complex waveform can be determined by two basic methods. Graphical Methodwhich can be used to find the RMS value of any non-sinusoidal time-varying waveform by drawing a number of mid-ordinates onto the waveform. Analytical Methodis a mathematical procedure for finding the effective or RMS value of any periodic voltage or current using calculus.

Q&A1. As the generator coil rotates 360, theoutputvoltage goes through one complete cycle.In one cycle, the voltage increases from zero to Emaxin onedirection, decreases to zero, increasesto Emaxin the opposite direction (negative Emax), and then decreases to zero again. The valueof Emaxoccurs at 90 and is referred to as peak voltage. The time it takes for the generator tocomplete one cycle is called theperiod, and the number of cycles per second is called thefrequency(measured inhertz).

2. When used to compare the equivalent RMS voltage value of an alternating sinusoidal waveform that supplies the same electrical power to a given load as an equivalent DC circuit, the RMS value is called the effective value and is generally presented as:VefforIeff.

RESITANCE AND INDUCTANCE OF COIL

The growth of the current flowing through the inductor is not instant but is determined by the inductors ownself-induced or back emf value. Then for an inductor coil, this back emf voltageVLis proportional to therate of change of the currentflowing through it.This current will continue to rise until it reaches its maximum steady state condition which is around five time constants when this self-induced back emf has decayed to zero. At this point a steady state current is flowing through the coil, nomoreback emf is induced to oppose the current flow and therefore, the coil acts more like a short circuit allowing maximum current to flow through it.However, in an alternating current circuit which contains anAC Inductance, the flow of current through an inductor behaves very differently to that of a steady state DC voltage. Now in an AC circuit, the opposition to the current flowing through the coils windings not only depends upon the inductance of the coil but also the frequency of the applied voltage waveform as it varies from its positive to negative values.The actual opposition to the current flowing through a coil in an AC circuit is determined by theAC Resistanceof the coil with thisAC resistancebeing represented by a complex number. But to distinguish a DC resistance value from an AC resistance value, which is also known as Impedance, the termReactanceis used.Like resistance, reactance is measured in Ohms but is given the symbolXto distinguish it from a purely resistiveRvalue and as the component in question is an inductor, the reactance of an inductor is calledInductive Reactance, (XL) and is measured in Ohms. Its value can be found from the formula.Inductive Reactance

Where:XLis the Inductive Reactance in Ohms,is the frequency in Hertz andLis the inductance of the coil in Henries.We can also define inductive reactance in radians, where Omega,equals2.

So whenever a sinusoidal voltage is applied to an inductive coil, the back emf opposes the rise and fall of the current flowing through the coil and in a purely inductive coil which has zero resistance or losses, this impedance (which can be a complex number) is equal to its inductive reactance. Also reactance is represented by a vector as it has both a magnitude and a direction (angle).