Unit Ii Ac Circuits
Unit Ii Ac Circuits
Introduction to AC circuits:
“AC” stands for Alternating Current, which can refer to either voltage or current that alternates in
polarity or direction, respectively. These experiments are designed to introduce you to several
important concepts specific to AC.
A convenient source of AC voltage is household wall-socket power, which presents significant shock
hazard. In order to minimize this hazard while taking advantage of the convenience of this source of
AC, a small power supply will be the first project, consisting of a transformer that steps the
hazardous voltage (230 to 240 volts AC, RMS) down to 12 volts or less. The title of “power supply”
is somewhat misleading. This device does not really act as a source or supply of power, but rather as
a power converter, to reduce the hazardous voltage of wall-socket power to a much safer level.
When a battery is connected to a circuit, the current flows steadily in one direction. It is called a
direct current. Electric generators at electric power plants, however, produce alternating current due
to many technical reasons. Alternating current results when a sinusoidal e.m.f or voltage is applied in
a circuit. Circuits fed by the alternating source are known as A.C. circuits. Alternating current (AC)
circuits carry energy due to the coordinated vibrations of neighboring electrons. While DC circuits
require single electrons to (slowly) move through the circuit and carry energy thanks to the kinetic
energy carried by electrons as they drift through the wire, AC manages to carry energy without any
overall motion of the electrons through the circuit.
Alternating Current and E.M.F:
The current or e.m.f., whose magnitude changes with time and direction reverses periodically is
known as alternating current or e.m.f.;
The instantaneous values of alternating current and e.m.f at any time t are given by;
where I0 and E0 are their maximum value or peak value or amplitude of current and e.m.f respectively.
Their angular frequency is called driving frequency and is given by;
ω = 2π/T
Where T is time period and f is frequency of alternating current or e.m.f.
Advantages:
Generation, transmission, and distribution of A.C. are more economical than that of D.C.
AC is easily convertible into D.C.
AC can be better controlled without any loss of electric power by using a choke coil.
The alternating high voltage can be stepped down or stepped up easily by using a transformer.
AC. can reach distant places without much loss of electric power by using a transformer.
AC. machines are easier to use.
Disadvantages:
A.C. cannot be used in the electrolysis process such as electroplating, electrotyping, and
electrorefining etc. where only D.C. is used.
A.C. can be more dangerous than D.C. in terms of its attractive nature and also because its
maximum value is 2–√2 times its effective value.
A.C. in a wire is not uniformly distributed through its cross-section. The a.c. density is much
greater near the surface of the wire than that inside the wire. The a.c. density is much greater
near the surface of the wire than that inside the wire. The concentration of a.c. near the
surface of the wire is called the skin effect.
Markings on the scales of A.C. meters are not equidistant for small measurement
RMS Voltage Analytical Method: The graphical method above is a very good way of finding the
effective or RMS voltage, (or current) of an alternating waveform that is not symmetrical or
sinusoidal in nature. In other words the waveform shape resembles that of a complex waveform.
However, when dealing with pure sinusoidal waveforms we can make life a little bit easier for
ourselves by using an analytical or mathematical way of finding the RMS value.
A periodic sinusoidal voltage is constant and can be defined as V(t) = Vmax*cos(ωt) with a period of T.
Then we can calculate the root-mean-square (rms) value of a sinusoidal voltage (V(t)) as:
Then the RMS voltage (VRMS) of a sinusoidal waveform is determined by multiplying the peak voltage
value by 0.7071, which is the same as one divided by the square root of two ( 1/√2 ). The RMS
voltage, which can also be referred to as the effective value, depends on the magnitude of the
waveform and is not a function of either the waveforms frequency nor its phase angle.
Power and power factor:
Electrical power consumed in an AC circuit can be represented by the three sides of a right angled
triangle, known commonly as a power triangle:
We saw in our tutorial about Electrical Power that AC circuits which contain resistance and
capacitance or resistance and inductance, or both, also contain real power and reactive power. So in
order for us to calculate the total power consumed, we need to know the phase difference between the
sinusoidal waveforms of the voltage and current.
In an AC circuit, the voltage and current waveforms are sinusoidal so their amplitudes are constantly
changing over time. Since we know that power is voltage times the current (P = V*I), maximum
power will occur when the two voltage and current waveforms are lined up with each other. That is,
their peaks and zero crossover points occur at the same time. When this happens the two waveforms
are said to be “in-phase”.
The three main components in an AC circuit which can affect the relationship between the voltage
and current waveforms, and therefore their phase difference, by defining the total impedance of the
circuit are the resistor, the capacitor and the inductor.
The impedance, (Z) of an AC circuit is equivalent to the resistance calculated in DC circuits, with
impedance given in ohms. For AC circuits, impedance is generally defined as the ratio of the voltage
and current phasor’s produced by a circuit component. Phasor’s are straight lines drawn in such a way
as to represents a voltage or current amplitude by its length and its phase difference with respect to
other phasor lines by its angular position relative to the other phasor’s.
AC circuits contain both resistance and reactance that are combined together to give a total impedance
(Z) that limits current flow around the circuit. But an AC circuits impedance is not equal to the
algebraic sum of the resistive and reactive ohmic values as a pure resistance and pure reactance are
90o out-of-phase with each other. But we can use this 90o phase difference as the sides of a right
angled triangle, called an impedance triangle, with the impedance being the hypotenuse as determined
by Pythagoras theorem.
This geometric relationship between resistance, reactance and impedance can be represented visually
by the use of an impedance triangle as shown.
Note that impedance, which is the vector sum of the resistance and reactance, has not only a
magnitude (Z) but it also has a phase angle (θ), which represents the phase difference between the
resistance and the reactance. Also note that the triangle will change shape due to variations in
reactance, (X) as the frequency changes. Of course, resistance (R) will always remain constant.
We can take this idea one step further by converting the impedance triangle into a power triangle
representing the three elements of power in an AC circuit. Ohms Law tells us that in a DC circuit,
power (P), in watts, is equal to the current squared (I 2) times the resistance (R). So we can multiply
the three sides of our impedance triangle above by I2 to obtain the corresponding power triangle as:
Single phase and three-phase balanced circuits & Three phase loads :
In electrical engineering, three-phase electric power systems have at least three conductors
carrying alternating current voltages that are offset in time by one-third of the period. A three-phase
system may be arranged in delta (∆) or star (Y) (also denoted as wye in some areas). A wye system
allows the use of two different voltages from all three phases, such as a 230/400 V system which
provides 230 V between the neutral (centre hub) and any one of the phases, and 400 V across any two
phases. A delta system arrangement only provides one voltage magnitude, however it has a greater
redundancy as it may continue to operate normally with one of the three supply windings offline,
albeit at 57.7% of total capacity. Harmonic current in the neutral may become very large if non-linear
loads are connected.
One voltage cycle of a three-phase system, labeled 0 to 360° (2π radians) along the time axis. The
plotted line represents the variation of instantaneous voltage (or current) with respect to time. This
cycle repeats with a frequency that depends on the power system.
The Conversion or transformation or replacement of the Star connected load network to a Delta
connected network and similarly a Delta connected network to a Star Network is done by Star to Delta
or Delta to Star Conversion.
In star to delta conversion, the star connected load is to be converted into delta connection. Suppose
we have a Star connected load as shown in the figure An above, and it has to be converted into a Delta
connection as shown in figure B. The following Delta values are as follows.
Hence, if the values of ZA, ZB and ZC are known, therefore by knowing these values and by putting
them in the above equations, you can convert a star connection into a delta connection.
Delta to Star Conversion: Similarly, a Delta connection network is given as shown above, in figure B
and it has to be transformed into a Star connection, as shown above, in the figure A. The following
formulas given below are used for the conversion.
If the values of Z1, Z2 and Z3 are given, then by putting these values of the Impedances in the above
equations, the conversion of delta connection into star connection can be performed. As Impedance
(Z) is the vector quantity, therefore all the calculations are done in Polar and Rectangular form.
The sum of each of the voltages (and currents) at the star point is always zero. In a balanced system,
the neutral current and neutral power is zero. You can think of a balanced three-phase system as three
single-phase systems connected to a neutral line.
Each voltage lags the previous one by 120° (look at the zero crossings). The motor also again
introduces its own 30° phase shift between voltage and current.
Safety regulations for wiring installation vary widely around the world, with national, regional, and
municipal rules sometimes in effect. Some places allow the homeowner to install some or all of the
wiring in a home; other jurisdictions require electrical wiring to be installed by
licensed electricians only.
In new home construction, wiring for all electrical services can be easily installed before the walls are
finished. In existing buildings, installation of a new system, such as a security system or home theatre,
may require additional effort to install concealed wiring. Multiple unit dwellings such as
condominiums and apartment houses may have additional installation complexity in distributing
services within a house.
Services commonly found include:
Home theater
Distributed audio
Security monitoring
Security CCTV
Automation
Energy management
Power and telecommunication services generally require entry points into the home and a
location for connection equipment. For electric power supply, a cable is run either overhead or
underground into a distribution board in the home. A distribution board, or circuit breaker panel,
is typically a metal box mounted on a wall of the home. In many new homes the location of the
electrical switchboard is on the outside of the external wall of the garage.
The following home services are supported by discrete wiring systems [2]
Materials of wiring:
Electrical wiring is an electrical installation of cabling and associated devices such as switches,
distribution boards, sockets and light fittings in a structure.
Wiring is subject to safety standards for design and installation. Allowable wire and cable types and
sizes are specified according to the circuit operating voltage and electric current capability, with
further restrictions on the environmental conditions, such as ambient temperature range, moisture
levels, and exposure to sunlight and chemicals.
Associated circuit protection, control and distribution devices within a building's wiring system are
subject to voltage, current and functional specification. Wiring safety codes vary by locality, country
or region. The International Electrotechnical Commission (IEC) is attempting to harmonise wiring
standards amongst member countries, but significant variations in design and installation
requirements still exist.
Materials for wiring interior electrical systems in buildings vary depending on :
Wiring systems in a single family home or duplex, for example, are simple, with relatively low power
requirements, infrequent changes to the building structure and layout, usually with dry, moderate
temperature and non-corrosive environmental conditions. In a light commercial environment, more
frequent wiring changes can be expected, large apparatus may be installed and special conditions of
heat or moisture may apply. Heavy industries have more demanding wiring requirements, such as
very large currents and higher voltages, frequent changes of equipment layout, corrosive, or wet or
explosive atmospheres. In facilities that handle flammable gases or liquids, special rules may govern
the installation and wiring of electrical equipment in hazardous areas.
Wires and cables are rated by the circuit voltage, temperature rating and environmental conditions
(moisture, sunlight, oil, chemicals) in which they can be used. A wire or cable has a voltage (to
neutral) rating and a maximum conductor surface temperature rating. The amount of current a cable or
wire can safely carry depends on the installation conditions.
Modern wiring materials: Modern non-metallic sheathed cables, such as (US and Canadian) Types
NMB and NMC, consist of two to four wires covered with thermoplastic insulation, plus a bare wire
for grounding (bonding), surrounded by a flexible plastic jacket. Some versions wrap the individual
conductors in paper before the plastic jacket is applied.
Special versions of non-metallic sheathed cables, such as US Type UF, are designed for direct
underground burial (often with separate mechanical protection) or exterior use where exposure
to ultraviolet radiation (UV) is a possibility. These cables differ in having a moisture-resistant
construction, lacking paper or other absorbent fillers, and being formulated for UV resistance.
Rubber-like synthetic polymer insulation is used in industrial cables and power cables installed
underground because of its superior moisture resistance.
Insulated cables are rated by their allowable operating voltage and their maximum operating
temperature at the conductor surface. A cable may carry multiple usage ratings for applications, for
example, one rating for dry installations and another when exposed to moisture or oil.
Generally, single conductor building wire in small sizes is solid wire, since the wiring is not required
to be very flexible. Building wire conductors larger than 10 AWG (or about 6 mm²) are stranded for
flexibility during installation, but are not sufficiently pliable to use as appliance cord.
Cables for industrial, commercial and apartment buildings may contain many insulated conductors in
an overall jacket, with helical tape steel or aluminium armour, or steel wire armour, and perhaps as
well an overall PVC or lead jacket for protection from moisture and physical damage. Cables intended
for very flexible service or in marine applications may be protected by woven bronze wires. Power or
communications cables (e.g., computer networking) that are routed in or through air-handling spaces
(plenums) of office buildings are required under the model building code to be either encased in metal
conduit, or rated for low flame and smoke production.
Copper conductors:
Electrical devices often contain copper conductors because of their multiple beneficial properties,
including their high electrical conductivity, tensile strength, ductility, creep resistance, corrosion
resistance, thermal conductivity, coefficient of thermal expansion, solderability, resistance
to electrical overloads, compatibility with electrical insulators and ease of installation.
Aluminium conductors:
Terminal blocks for joining aluminium and copper conductors. The terminal blocks may be mounted
on a DIN rail.
Aluminium wire was common in North American residential wiring from the late 1960s to mid-1970s
due to the rising cost of copper. Because of its greater resistivity, aluminium wiring requires larger
conductors than copper. For instance, instead of 14 AWG (American wire gauge) copper wire,
aluminium wiring would need to be 12 AWG on a typical 15 ampere lighting circuit, though local
building codes vary.
Cable runs:
Insulated wires may be run in one of several forms between electrical devices. This may be a
specialised bendable pipe, called a conduit, or one of several varieties of metal (rigid steel or
aluminium) or non-metallic (PVC or HDPE) tubing. Rectangular cross-section metal or PVC wire
troughs (North America) or trunking (UK) may be used if many circuits are required. Wires run
underground may be run in plastic tubing encased in concrete, but metal elbows may be used in
severe pulls. Wiring in exposed areas, for example factory floors, may be run in cable trays or
rectangular raceways having lids.
The Staircase wiring diagram in a Traveller system or common system method is shown
below:
A Staircase wiring makes the feasibility for the user to turn ON and OFF the load from two
switches placed apart from each other.
The First pole and second pole of the SPDT switch S1 has connected to the corresponding
first and second pole of the SPDT switch S2. That is similar poles of both two switches are
connected each other.
The phase of the supply line is connected to the common pole of a switch. And the phase line
to the load is taken from the common pole of the next switch. It makes an arrangement that,
to close the circuit both the switches should be in the same position in order to make the two
common poles in contact to achieve a closed circuit. Changing ON & OFF condition of a
single switch can determine whether the circuit is closed or open. Thus in staircase wiring,
we can control the load from both positions. If a truth table has made for the above traveller
system output, it will have a result similar to an XNOR gate. That is the light ON’s when
both the switches are in the same position.
S1 S2 L1
0 0 OFF
1 0 ON
0 1 ON
1 1 OFF
Similarly, if the connections between the switch s1 and s2 have interchanged, the load will
ON when the switches have opposite positions.
A fluorescent lamp basically consists of a long glass gas discharge tube. Its inner
surface is coated with phosphorous and is filled with an inert gas, generally argon,
with a trace of mercury.
The tube is then finally sealed at low pressure with two filament electrodes each at its
both ends.
These electrode filaments are used to preheat the tube and initiate a rapid conduction
of electrons between the two end electrodes. The process initially requires a relatively
high amount of power.
The energy also converts some of the mercury from a liquid to a glass. Electrons then
collide with the gaseous mercury atoms, increasing the amount of energy. As
electrons return to their original energy level, they begin to release light. However, the
light they emit is ultraviolet, and not visible to the naked eye, so another step needs to
take place before we can see the light.
This is why the tube was coated with phosphorous. Phosphors will give off light when
exposed to light. When exposed to the ultraviolet light, the particles emit a white light
which we can see.
Once the conduction of electrons between the electrodes is complete, no more heating
of the filaments is required and whole system works at a much lower current.
Here is one example of a tube light fixture consisting of a large heavy square “choke”
or “ballast” and a small cylindrical “starter.” Let’s try to understand how the whole
system works. Please refer to the circuit diagram on the right as you read the
following points:
The choke is in fact a large inductor. It consists of a long copper winding over iron
laminations.
An inductor by nature always has a tendency to throw back the stored current in it,
every time the power through it is switched OFF. This principle of the choke is
exploited in lighting a fluorescent tube light.
When an AC voltage is applied to a tube light fixture, the voltage passes through the
choke, the starter, and the filaments of the tube.
The filaments light up and instantly warm up the tube. The starter is made up of a
discharbe bulb with two electrodes next to it. When electricity passes through it an
electrical arc is created between the two electrodes. This creates light, however the
heat from the bulb causes one of the electrodes (a bimetallic strip) to bend, making
contact with the other electrode. This stops the charged particles from creating the
electrical arc that created light. However, now that the heat from the light is gone, the
bimetallic strip cools and bends away from the electrode, opening the circuit again.
At this point, the ballast or choke “kick’s back” it’s stored current, which again passes
through the filaments and ignites the tube light once again.
If the tube does not sufficiently charge up, subsequent kicks are delivered by the
choke due to rapid switching of the starter, so that finally the tube strikes.
After this the choke only acts like a low impedance current limiter to the tube as long
as the light is kept illuminated.
A common problem associated with these types of fixtures is humming or buzzing.
The reason for this lies in the loosely fitted choke on to the fixture which vibrates in
accordance with the 50 or 60 hertz frequency of our AC mains and creates a humming
sort of noise. Tightening the choke’s screws may instantly eliminate the problem.
The working principle of today’s modern electronic ballasts is to avoid the use of starters
for the preheating purpose. They are also very light in weight. These inhibit the initial
flickering of the tube light as normally seen in the ordinary tube fixtures by changing the
frequency of the mains power to a much higher 20,000 hertz or more. Moreover,
electronic ballasts are very energy efficient.
1. Fluorescent Tube
2. Ballast
3. Starter
The starter is like a key of fluorescent light because it is used to light up the tube. When
we connect the AC supply voltage to the circuit, then the starter act like short circuited
and current flow through those filament (located at the first and second end of the tube
light) and the filament generate heat and it ionized the gas (mercury vapor) in the
fluorescent tube lamp. So the gas becomes electrically conductive medium. At the same
time when the starter opened the circuit path of two filaments from series connected, then
the ballast release its stored voltage. And it makes the fluorescent tube fully lighten. Now
the starter has no job in the circuit, if you open it from the circuit the fluorescent tube
light will be still lighten, until you release the main supply.
Fuse
Circuit Breaker
PolySwitch
RCCB
Metal Oxide Varistor
Inrush Current Limiter
Gas Discharge Tube
Spark Gap
Lightning Arrester
Fuse
In electrical circuits, a fuse is an electrical device used to protect the circuit from overcurrent.
It consists of a metal strip that liquefies when the flow of current through it is high. Fuses are
essential electrical devices, and there are different types of fuses available in the market today
based on specific voltage and current ratings, application, response time, and breaking
capacity.
The characteristics of fuses like time and current are selected to give sufficient protection
without unnecessary disruption. Please refer the link to know more about: Different Types of
Fuses and Its Applications.
Circuit Breaker
A circuit breaker is one kind of electrical switch used to guard an electrical circuit against
short circuit otherwise an overload which will cause by excess current supply. The basic
function of a circuit breaker is to stop the flow of current once a fault has occurred. Not like a
fuse, a circuit breaker can be operated either automatically or manually to restart regular
operation.
Circuit breakers are available in different sizes from small devices to large switch gears
which are used to protect low current circuits as well as high voltage circuits. Please refer the
link to know more about: Types of Circuit Breaker and Its Importance.
RCCB or RCD
The RCD-residual current device (or) RCCB- residual current circuit breaker is a safety
device which notices a problem in your home power supply then turns OFF in 10-15
milliseconds to stop electric shock. A residual current device does not give safety against
short circuit or overload in the circuit, so we cannot change a fuse instead of RCD.
RCDs are frequently incorporated with some type of circuit breaker like an MCB (miniature
circuit breaker) or a fuse, which guards against overload current in the circuit. The residual
current device also cannot notice a human being due to by mistake touching both conductors
at a time.
They present a high resistance firstly, which stops huge currents from flowing by turn-on.
Because the flow of current will continues, NTC thermistors heat-up, permitting high flow of
current throughout normal operation. These thermistors are generally much superior to
measurement kind thermistors, which are intentionally planned for power applications.
Lightning Protection:
The lightning protection includes MOV (metal oxide varistor) and gas discharge tube
An expulsion lamp is an electrical device which uses a gas-filled tube such as metal halide
lamps, fluorescent lamps, neon lights, and sodium-vapor lamps. Specific gas-filled tubes
namely thyratrons, ignitrons, and krytrons are employed as switching devices in various
electrical devices.
The required voltage to begin and maintain discharge is reliant on the force, geometry of the
tube, and composition of the fill gas. Even though the cover is normally glass, power tubes
frequently employ ceramics, as well as military tubes frequently employ glass wrinkled
metal.
Underground Feeder Cable : These cables are quite similar to NM cables, but
instead of each wire being individually wrapped in thermoplastic, wires are grouped
together and embedded in the flexible material. Available in a variety of gauge sizes,
UF cables are often used for outdoor lighting and in-ground applications. Their high
water-resistance makes them ideal for damp areas like gardens as well as open-to-air
lamps, pumps, etc.
Multi-Conductor Cable : This is a cable type that is commonly used in homes, since
it is simple to use and well-insulated. Multi-conductor or multi-core (MC) cables
feature more than one conductor, each of which is insulated individually. In addition,
an outer insulation layer is added for extra security. Different varieties are used in
industries, like the audio multicore ‘snake cable’ used in the music industry.
Coaxial Cable : A coaxial (sometimes heliax) cable features a tubular insulating layer
that protects an inner conductor which is further surrounded by a tubular conducting
shield, and might also feature an outer sheath for extra insulation. Called ‘coaxial’
since the two inner shields share the same geometric axis, these cables are normally
used for carrying television signals and connecting video equipment.
Unshielded Twisted Pair Cable : Like the name suggests, this type consists of two
wires that are twisted together. The individual wires are not insulated, which makes
this cable perfect for signal transmission and video applications. Since they are more
affordable than coaxial or optical fiber cables, UTP cables are often used in
telephones, security cameras and data networks. For indoor use, UTP cables with
copper wires or solid copper cores are a popular choice, since they are flexible and
can be easily bent for in-wall installation.
Ribbon Cable : Ribbon cables are often used in computers and peripherals, with
various conducting wires that run parallel to each other on a flat plane, leading to a
visual resemblance to flat ribbons. These cables are quite flexible and can only handle
low voltage applications.
Twin-Lead Cable : These are flat two-wire cables that are used for transmission
between an antenna and receiver, like TV and radio.
Twinaxial Cable : This is a variant of coaxial cables, which features two inner
conductors instead of one and is used for very-short-range high-speed signals.
Paired Cable : With two individually insulated conductors, this cable is normally
used in DC or low-frequency AC applications.
Twisted Pair : This cable is similar to paired cables, but the inner insulated wires are
twisted or intertwined.
2. Cable Color Code – Color coding of cable insulation is done to determine active, neutral
and earth conductors. The NEC has not prescribed any color for phase/active conductors.
Different countries/regions have different cable color coding, and it is essential to know what
is applicable in your region. However, active conductors cannot be green/yellow, green,
yellow, light blue or black..
Cable Size – Cable size is the gauge of individual wires within the cable, such as 14, 12, 10
etc. – again, the bigger the number, the smaller the size. The number of wires follows the
wire-gauge on a cable. So, 10/3 would indicate the presence of 3 wires of 10-gauge within the
cable. Ground wire, if present, is not indicated by this number, and is represented by the letter
‘G’.
Safety is very important, and if your installation of wires and cables is not proper, it could
lead to accidents. Before you start any electrical project that includes wiring and cabling, you
need to obtain permission from your local building inspector. Once the job is done, get the
installation inspected for compliance with local codes and regulations.