Ch 2 direct current & basic ac theory

CHAPTER TWO

(CH2)

Direct current & Basic AC theory

Direct current or DC electricity is the continuous movement of electrons from an area of negative (−) charges to an area of positive (+) charges through a conducting material such as a metal wire. Whereas static electricity sparks consist of the sudden movement of electrons from a negative to positive surface, DC electricity is the continuous movement of the electrons through a wire.

( DC )Direct Current

A DC circuit is necessary to allow the current or steam of electrons to flow. Such a circuit consists of a source of electrical energy (such as a battery) and a conducting wire running from the positive end of the source to the negative terminal. Electrical devices may be included in the circuit. DC electricity in a circuit consists of voltage, current and resistance. The flow of DC electricity is similar to the flow of water through a hose.


Direct current is the one way flow of electrical charge from a positive to a negative charge .

Batteries produce direct current.

Direct Current is different than alternating current because the charge only flows in one direction.

Thomas Edison is credited for promoting direct current.


Thomas Alva Edison (1847–1931)

http://en.wikipedia.org/wiki/Direct_current

http://en.wikipedia.org/wiki/Electrical_charge

http://en.wikipedia.org/wiki/Battery_(electrical)

http://en.wikipedia.org/wiki/Thomas_Edison

Ohm’s Law for DC


Alternating current (AC) electricity is the type of electricity commonly used in homes and businesses throughout the world. While direct current (DC) electricity flows in one direction through a wire, AC electricity alternates its direction in a back-and-forth motion. The direction alternates between 50 and 60 times per second, depending on the electrical system of the country.

(AC )Alternating Current

AC electricity is created by an AC electric generator, which determines the frequency. What is special about AC electricity is that the voltage can be readily changed, thus making it more suitable for long-distance transmission than DC electricity. But also, AC can employ capacitors and inductors in electronic circuitry, allowing for a wide range of applications


NOTE : Now with using the VFD Drives system we can using it to transfer the power by DC and connected between different frequency system



Power Plant

Mathematics of ACThe output of an AC supply is

sinusoidal and varies with time according to the following equation

◦V (t) = Vmax sin ωt ◦Where

◦ωt = 2ƒt◦V(t) is the instantaneous

voltageVmax is the maximum

voltage of the supply(Peak Value)

ƒ is the frequency at which the voltage changes, in Hz


(AC )Alternating CurrentConsider a circuit

consisting of an AC source and a resistor

The graph shows the current through and the voltage across the resistor

The current and the voltage reach their maximum values at the same time

The current and the voltage are said to be in phase

The rms current is the direct current that would dissipate the same amount of energy in a resistor as is actually dissipated by the AC current


maxmax0.707

2rms

II I

Alternating voltages can also be discussed in terms of rms values

maxmax0.707

2rms

VV V

Circuit Elements, Impedance and Phase Angles


Ohm’s Law in an AC Circuitrms values will be used when

discussing AC currents and voltages

◦AC ammeters and voltmeters are designed to read rms values

◦Many of the equations will be in the same form as in DC circuits

Ohm’s Law for a resistor, R, in an AC circuit

◦ΔVR,rms = Irms RAlso applies to the maximum values

of v and i


Phase Diagram



Capacitors in an AC Circuit

The current reverses direction

The voltage across the plates decreases as the plates lose the charge they had accumulated

The voltage across the capacitor lags behind the current by 90°


Phase Diagram


AC Capacitive LoadSo we now know that capacitors oppose changes in voltage with the

flow of electrons through the capacitor being directly proportional to the rate of voltage change across its plates as the capacitor charges and discharges. Unlike a resistor where the opposition to current flow is its actual resistance, the opposition to current flow in a capacitor is called Reactance. Like resistance, reactance is measured in Ohm's but is given the symbol X to distinguish it from a purely resistive R value and as the component in question is a capacitor, the reactance of a capacitor is called Capacitive Reactance, ( XC ) which is measured in Ohms.

Since capacitors pass current through themselves in proportion to the rate of voltage change, the faster the voltage changes the more current they will pass. Likewise, the slower the voltage changes the less current they will pass. This means then that the reactance of a capacitor is "inversely proportional" to the frequency of the supply as shown.


From the above formula we can see that the value of capacitive reactance and therefore its overall impedance ( in Ohms ) decreases towards zero as the frequency increases acting like a short circuit. Likewise, as the frequency approaches zero or DC, the capacitors reactance increases to infinity, acting like an open circuit which is why

capacitors block DC


AC Inductance & Inductive Reactance


Consider an AC circuit with a source and an inductor

The current in the circuit is impeded by the back emf of the inductor

The voltage across the inductor always leads the current by 90°

Phase Diagram


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)


The RLC Series CircuitThus far we have seen that the three basic passive

components, R, L and C have very different phase relationships to each other when connected to a sinusoidal AC supply. In a pure ohm resistor the voltage waveforms are "in-phase" with the current. In a pure inductance the voltage waveform "leads" the current by 90o , In a pure capacitance the voltage waveform "lags" the current by 90o.

This Phase Difference, Φ depends upon the reactive value of the components being used and hopefully by now we know that reactance, ( X ) is zero if the element is resistive, positive if the element is inductive and negative if the element is capacitive giving the resulting impedance values as:


http://www.electronics-tutorials.ws/accircuits/phase-difference.html

(AC )Alternating Currentwe can combine all three together into a series RLC circuit. The analysis of a series RLC circuit is the same as that for the dual series RL and RC circuits we looked at previously, except this time we need to take into account the magnitudes of both XL and XC to find the overall circuit reactance. Series RLC circuits are classed as second-order circuits because they contain two energy storage elements, an inductance L and a capacitance C. Consider the RLC circuit below.

The series RLC circuit above has a single loop with the instantaneous current flowing through the loop being the same for each circuit element. Since the inductive and capacitive reactance's are a function of frequency, the sinusoidal response of a series RLC circuit will vary with the applied frequency, ( ƒ ). Therefore the individual voltage drops across each circuit element of R, L and C element will be "out-of-phase" with each other as defined by:

i(t) = Imax sin(ωt) , The instantaneous voltage across a pure resistor, VR is "in-phase" with the current.

The instantaneous voltage across a pure inductor, VL "leads" the current by 90o

The instantaneous voltage across a pure capacitor, VC "lags" the current by 90o

Therefore, VL and VC are 180o "out-of-phase" and in opposition to each other.Then the amplitude of the source voltage across all three components in a

series RLC circuit is made up of the three individual component voltages, VR, VL and VC with the current common to all three components. The vector diagrams will therefore have the current vector as their reference with the three voltage vectors being plotted with respect to this reference as shown below.


This means then that we can not simply add together VR, VL and VC to find the supply voltage, VS across all three components as all three voltage vectors point in different directions with regards to the current vector. Therefore we will have to find the supply voltage, VS as the Phasor Sum of the three component voltages combined together

vectorially.


Kirchoff's voltage law ( KVL ) for both loop and nodal circuits states that around any closed loop the sum of voltage drops around the loop equals the sum of the EMF's. Then applying this law to the these three voltages will give us the amplitude of the source voltage, VS as.


KVL : VS - VL - VR - VC = 0

KVL : VS = VL + VR + VC

The Impedance of a Series RLC CircuitAs the three vector voltages are out-of-phase with each other, XL, XC and R

must also be "out-of-phase" with each other with the relationship between R, XL and XC being the vector sum of these three components thereby giving us the circuits overall impedance, Z. These circuit impedances can

be drawn and represented by an Impedance Triangle as shown below.


The impedance Z of a series RLC circuit depends upon the angular frequency, ω as do XL and XC If the capacitive reactance is greater than the inductive reactance, XC > XL then the overall circuit reactance is capacitive giving a leading phase angle. Likewise, if the inductive reactance is greater than the capacitive reactance, XL > XC then the overall circuit reactance is inductive giving the series circuit a lagging phase angle. If the two reactance's are the same and XL = XC then the angular frequency at which this occurs is called the resonant frequency and produces the effect of resonance which we will look at in more detail in another tutorial.


Then the magnitude of the current depends upon the frequency applied to the series RLC circuit. When impedance, Z is at its maximum, the current is a minimum and likewise, when Z is at its minimum, the current is at maximum. So the above equation for impedance can be re-written as:


The phase angle, θ between the source voltage, VS and the current, i is the same as for the angle between Z and R in the impedance triangle. This phase angle may be positive or negative in value depending on whether the source voltage leads or lags the circuit current and can be calculated mathematically from the ohm values of the impedance triangle as:


Example A series RLC circuit containing a resistance of 12Ω, an

inductance of 0.15H and a capacitor of 100uF are connected in series across a 100V, 50Hz supply. Calculate the total circuit impedance, the circuits current, power

factor and draw the phasor diagram.


Power TriangleThe power triangle graphically shows the relationship between real (P), reactive (Q) and apparent power (S).S = P + JQS (Total Power)P (Active Power)Q (Reactive Power)


The power triangle also shows that we can find real (P) and reactive (Q) power, given S and the impedance angle φ .

NOTE: The impedance angle and the “power factor angle” are the same value!

S = P + JQS = V*I P=V*I*Cos φ Q=V*I*Sin φ The Resistance load is pure power factor so Cos φ will be equal one & for pure inductive load the power factor will be zero so the active power is zero and reactive power is max To improve power factor by adding banking capacitor


Date post:	08-Aug-2015
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Ch 2 direct current & basic ac theory

Engineering