AC CURRENT

AC CURRENT

Most students of electricity begin their study with what is known as direct current (DC), which is electricity flowing in a constant direction, and/or possessing a voltage with constant polarity. DC is the kind of electricity made by a battery (with definite positive and negative terminals), or the kind of charge generated by rubbing certain types of materials against each other.

As useful and as easy to understand as DC is, it is not the only “kind” of electricity in use. Certain sources of electricity (most notably, rotary electro-mechanical generators) naturally produce voltages alternating in polarity, reversing positive and negative over time. Either as a voltage switching polarity or as a current switching direction back and forth, this “kind” of electricity is known as Alternating Current (AC): Figure below

Direct vs alternating current

Whereas the familiar battery symbol is used as a generic symbol for any DC voltage source, the circle with the wavy line inside is the generic symbol for any AC voltage source.

One might wonder why anyone would bother with such a thing as AC. It is true that in some cases AC holds no practical advantage over DC. In applications where electricity is used to dissipate energy in the form of heat, the polarity or direction of current is irrelevant, so long as there is enough voltage and current to the load to produce the desired heat (power dissipation). However, with AC it is possible to build electric generators, motors and power distribution systems that are far more efficient than DC, and so we find AC used predominately across the world in high power applications. To explain the details of why this is so, a bit of background knowledge about AC is necessary.

If a machine is constructed to rotate a magnetic field around a set of stationary wire coils with the turning of a shaft, AC voltage will be produced across the wire coils as that shaft is rotated, in accordance with Faraday's Law of electromagnetic induction. This is the basic operating principle of an AC generator, also known as an alternator: Figure below

Alternator operation

Notice how the polarity of the voltage across the wire coils reverses as the opposite poles of the rotating magnet pass by. Connected to a load, this reversing voltage polarity will create a reversing current direction in the circuit. The faster the alternator's shaft is turned, the faster the magnet will spin, resulting in an alternating voltage and current that switches directions more often in a given amount of time.

While DC generators work on the same general principle of electromagnetic induction, their construction is not as simple as their AC counterparts. With a DC generator, the coil of wire is mounted in the shaft where the magnet is on the AC alternator, and electrical connections are made to this spinning coil via stationary carbon “brushes” contacting copper strips on the rotating shaft. All this is necessary to switch the coil's changing output polarity to the external circuit so the external circuit sees a constant polarity: Figure below

DC generator operation

The generator shown above will produce two pulses of voltage per revolution of the shaft, both pulses in the same direction (polarity). In order for a DC generator to produce constant voltage, rather than brief pulses of voltage once every 1/2 revolution, there are multiple sets of coils making intermittent contact with the brushes. The diagram shown above is a bit more simplified than what you would see in real life.

The problems involved with making and breaking electrical contact with a moving coil should be obvious (sparking and heat), especially if the shaft of the generator is revolving at high speed. If the atmosphere surrounding the machine contains flammable or explosive vapors, the practical problems of spark-producing brush contacts are even greater. An AC generator (alternator) does not require brushes and commutators to work, and so is immune to these problems experienced by DC generators.

The benefits of AC over DC with regard to generator design is also reflected in electric motors. While DC motors require the use of brushes to make electrical contact with moving coils of wire, AC motors do not. In fact, AC and DC motor designs are very similar to their generator counterparts (identical for the sake of this tutorial), the AC motor being dependent upon the reversing magnetic field produced by alternating current through its stationary coils of wire to rotate the rotating magnet around on its shaft, and the DC motor being dependent on the brush contacts making and breaking connections to reverse current through the rotating coil every 1/2 rotation (180 degrees).

So we know that AC generators and AC motors tend to be simpler than DC generators and DC motors. This relative simplicity translates into greater reliability and lower cost of manufacture. But what else is AC good for? Surely there must be more to it than design details of generators and motors! Indeed there is. There is an effect of electromagnetism known as mutual induction, whereby two or more coils of wire placed so that the changing magnetic field created by one induces a voltage in the other. If we have two mutually inductive coils and we energize one coil with AC, we will create an AC voltage in the other coil. When used as such, this device is known as a transformer: Figurebelow

Transformer “transforms” AC voltage and current.

The fundamental significance of a transformer is its ability to step voltage up or down from the powered coil to the unpowered coil. The AC voltage induced in the unpowered (“secondary”) coil is equal to the AC voltage across the powered (“primary”) coil multiplied by the ratio of secondary coil turns to primary coil turns. If the secondary coil is powering a load, the current through the secondary coil is just the opposite: primary coil current multiplied by the ratio of primary to secondary turns. This relationship has a very close mechanical analogy, using torque and speed to represent voltage and current, respectively: Figure below

Speed multiplication gear train steps torque down and speed up. Step-down transformer steps voltage down and current up.

If the winding ratio is reversed so that the primary coil has less turns than the secondary coil, the transformer “steps up” the voltage from the source level to a higher level at the load: Figure below

Speed reduction gear train steps torque up and speed down. Step-up transformer steps voltage up and current down.

The transformer's ability to step AC voltage up or down with ease gives AC an advantage unmatched by DC in the realm of power distribution in figure below. When transmitting electrical power over long distances, it is far more efficient to do so with stepped-up voltages and stepped-down currents (smaller-diameter wire with less resistive power losses), then step the voltage back down and the current back up for industry, business, or consumer use.

Transformers enable efficient long distance high voltage transmission of electric energy.

Transformer technology has made long-range electric power distribution practical. Without the ability to efficiently step voltage up and down, it would be cost-prohibitive to construct power systems for anything but close-range (within a few miles at most) use.

As useful as transformers are, they only work with AC, not DC. Because the phenomenon of mutual inductance relies on changing magnetic fields, and direct current (DC) can only produce steady magnetic fields, transformers simply will not work with direct current. Of course, direct current may be interrupted (pulsed) through the primary winding of a transformer to create a changing magnetic field (as is done in automotive ignition systems to produce high-voltage spark plug power from a low-voltage DC battery), but pulsed DC is not that different from AC. Perhaps more than any other reason, this is why AC finds such widespread application in power systems.

• REVIEW:
• DC stands for “Direct Current,” meaning voltage or current that maintains constant polarity or direction, respectively, over time.
• AC stands for “Alternating Current,” meaning voltage or current that changes polarity or direction, respectively, over time.
• AC electromechanical generators, known as alternators, are of simpler construction than DC electromechanical generators.
• AC and DC motor design follows respective generator design principles very closely.
• A transformer is a pair of mutually-inductive coils used to convey AC power from one coil to the other. Often, the number of turns in each coil is set to create a voltage increase or decrease from the powered (primary) coil to the unpowered (secondary) coil.
• Secondary voltage = Primary voltage (secondary turns / primary turns)
• Secondary current = Primary current (primary turns / secondary turns)

     Synchronous Motor Working Principle

Electrical motor in general is an electro-mechanical device that converts energy from electrical domain to mechanical domain. Based on the type of input we have classified it into single phase and 3 phase motors. Among 3 phase induction motors and synchronous motors are more widely used.

When a 3 phase electric conductors are placed in a certain geometrical positions (In certain angle from one another) there is an electrical field generate. Now the rotating magnetic field rotates at a certain speed, that speed is called synchronous speed. Now if an electromagnet is present in this rotating magnetic field, the electromagnet is magnetically locked with this rotating magnetic field and rotates with same speed of rotating field. Synchronous motors is called so because the speed of the rotor of this motor is same as the rotating magnetic field. It is basically a fixed speed motor because it has only one speed, which is synchronous speed and therefore no intermediate speed is there or in other words it’s in synchronism with the supply frequency. Synchronous speed is given by

Construction of Synchronous Motor

Normally it’s construction is almost similar to that of a 3 phase induction motor, except the fact that the rotor is given dc supply, the reason of which is explained later. Now, let us first go through the basic construction of this type of motor

From the above picture, it is clear that how this type of motors are designed. The stator is given is given three phase supply and the rotor is given dc supply.

Main Features of Synchronous Motors

1. Synchronous motors are inherently not self starting. They require some external means to bring their speed close to synchronous speed to before they are synchronized.
2. The speed of operation of is in synchronism with the supply frequency and hence for constant supply frequency they behave as constant speed motor irrespective of load condition
3. This motor has the unique characteristics of operating under anyelectrical power factor. This makes it being used in electrical power factorimprovement.

Principle of Operation Synchronous Motor

Synchronous motor is a doubly excited machine i.e two electrical inputs are provided to it. It’s stator winding which consists of a 3 phase winding is provided with 3 phase supply and rotor is provided with DC supply. The 3 phase stator winding carrying 3 phase currents produces 3 phase rotating magnetic flux. The rotor carrying DC supply also produces a constant flux. Considering the frequency to be 50 Hz, from the above relation we can see that the 3 phase rotating flux rotates about 3000 revolution in 1 min or 50 revolutions in 1 sec. At a particular instant rotor and stator poles might be of same polarity (N-N or S-S) causing repulsive force on rotor and the very next second it will be N-S causing attractive force. But due to inertia of the rotor, it is unable to rotate in any direction due to attractive or repulsive force and remain in standstill condition. Hence it is not self starting.

To overcome this inertia, rotor is initially fed some mechanical input which rotates it in same direction as magnetic field to a speed very close to synchronous speed. After some time magnetic locking occurs and the synchronous motor rotates in synchronism with the frequency.

Methods of Starting of Synchronous Motor

1. Synchronous motors are mechanically coupled with another motor. It could be either 3 phase induction motor or DC shunt motor. DC excitation is not fed initially. It is rotated at speed very close to its synchronous speed and after that DC excitation is given. After some time when magnetic locking takes place supply to the external motor is cut off.
2. Damper winding : In case, synchronous motor is of salient pole type, additional winding is placed in rotor pole face. Initially when rotor is standstill, relative speed between damper winding and rotating air gap flux in large and an emf is induced in it which produces the required starting torque. As speed approaches synchronous speed , emf and torque is reduced and finally when magnetic locking takes place, torque also reduces to zero. Hence in this case synchronous is first run as three phase induction motor using additional winding and finally it is synchronized with the frequency.

Application of Synchronous Motor

1. Synchronous motor having no load connected to its shaft is used forpower factor improvement. Owing to its characteristics to behave at anyelectrical power factor, it is used in power system in situations where static capacitors are expensive.
2. Synchronous motor finds application where operating speed is less (around 500 rpm) and high power is required. For power requirement from 35 kW to 2500 KW, the size, weight and cost of the correspondingthree phase induction motor is very high. Hence these motors are preferably used. Ex- Reciprocating pump, compressor, rolling mills etc.

Video-Working Principle of Synchronous Motor

Resistors in Series

Connecting Resistors in Series

Individual resistors can be connected together in either a series connection, a parallel connection or combinations of both series and parallel, to produce more complex resistor networks whose equivalent resistance is the mathematical combination of the individual resistors connected together.

Resistors in series or complicated Resistor Networks can be replaced by one single equivalent resistor, REQ or impedance, ZEQ and no matter what the combination or complexity of the resistor network is, all resistors obey the same basic rules as defined by Ohm’s Law and Kirchoff’s Circuit Laws.

Resistors in Series.

Resistors are said to be connected in “Series“, when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on. Then, resistors in series have a Common Current flowing through them as the current that flows through one resistor must also flow through the others as it can only take one path.

Then the amount of current that flows through a set of resistors in series will be the same at all points in a series resistor network. For example:

 

In the following example the resistors R1, R2 and R3 are all connected together in series between points A and B with a common current, I flowing through them.

Series Resistor Circuit

 

As the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, RT of the circuit must be equal to the sum of all the individual resistors added together. That is

and by taking the individual values of the resistors in our simple example above, the total equivalent resistance, REQ is therefore given as:

REQ = R1 + R2 + R3 = 1kΩ + 2kΩ + 6kΩ = 9kΩ

 

So we see that we can replace all three individual resistors above with just one single “equivalent” resistor which will have a value of 9kΩ.

Where four, five or even more resistors are all connected together in a series circuit, the total or equivalent resistance of the circuit, RT would still be the sum of all the individual resistors connected together and the more resistors added to the series, the greater the equivalent resistance (no matter what their value).

This total resistance is generally known as the Equivalent Resistance and can be defined as;  “a single value of resistance that can replace any number of resistors in series without altering the values of the current or the voltage in the circuit“. Then the equation given for calculating total resistance of the circuit when connecting together resistors in series is given as:

Series Resistor Equation

Rtotal = R1 + R2 + R3 + ….. Rn etc.

Note then that the total or equivalent resistance, RT has the same effect on the circuit as the original combination of resistors as it is the algebraic sum of the individual resistances.

If two resistances or impedances in series are equal and of the same value, then the total or equivalent resistance, RT is equal to twice the value of one resistor. That is equal to 2R and for three equal resistors in series, 3R, etc.

If two resistors or impedances in series are unequal and of different values, then the total or equivalent resistance, RT is equal to the mathematical sum of the two resistances. That is equal to R1 + R2. If three or more unequal (or equal) resistors are connected in series then the equivalent resistance is: R1 + R2 + R3 +…, etc.

 

One important point to remember about resistors in series networks to check that your maths is correct. The total resistance ( RT ) of any two or more resistors connected together in series will always be GREATER than the value of the largest resistor in the chain. In our example above RT = 9kΩ where as the largest value resistor is only 6kΩ.

Series Resistor Voltage

The voltage across each resistor connected in series follows different rules to that of the series current. We know from the above circuit that the total supply voltage across the resistors is equal to the sum of the potential differences across R1 , R2 and R3 , VAB = VR1 + VR2 + VR3 = 9V.

Using Ohm’s Law, the voltage across the individual resistors can be calculated as:

Voltage across R1 = IR1 = 1mA x 1kΩ = 1V

Voltage across R2 = IR2 = 1mA x 2kΩ = 2V

Voltage across R3 = IR3 = 1mA x 6kΩ = 6V

 

giving a total voltage VAB of ( 1V + 2V + 6V ) = 9V which is equal to the value of the supply voltage. Then the sum of the potential differences across the resistors is equal to the total potential difference across the combination and in our example this is 9V.

The equation given for calculating the total voltage in a series circuit which is the sum of all the individual voltages added together is given as:

Then series resistor networks can also be thought of as “voltage dividers” and a series resistor circuit having N resistive components will have N-different voltages across it while maintaining a common current.

By using Ohm’s Law, either the voltage, current or resistance of any series connected circuit can easily be found and resistor of a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor.

Resistors in Series Example No1

Using Ohms Law, calculate the equivalent series resistance, the series current, voltage drop and power for each resistor in the following resistors in series circuit.

 

All the data can be found by using Ohm’s Law, and to make life a little easier we can present this data in tabular form.

Resistance	Current	Voltage	Power
R1 = 10Ω	I1 = 200mA	V1 = 2V	P1 = 0.4W
R2 = 20Ω	I2 = 200mA	V2 = 4V	P2 = 0.8W
R3 = 30Ω	I3 = 200mA	V3 = 6V	P3 = 1.2W
RT = 60Ω	IT = 200mA	VS = 12V	PT = 2.4W

Then for the circuit above, RT = 60Ω, IT = 200mA, VS = 12V and PT = 2.4W

The Voltage Divider Circuit

We can see from the above example, that although the supply voltage is given as 12 volts, different voltages, or voltage drops, appear across each resistor within the series network. Connecting resistors in series like this across a single DC supply has one major advantage, different voltages appear across each resistor producing a very handy circuit called a Voltage Divider Network.

This simple circuit splits the supply voltage proportionally across each resistor in the series chain with the amount of voltage drop being determined by the resistors value and as we now know, the current through a series resistor circuit is common to all resistors. So a larger resistance will have a larger voltage drop across it, while a smaller resistance will have a smaller voltage drop across it.

The series resistive circuit shown above forms a simple voltage divider network were three voltages 2V, 4V and 6V are produced from a single 12V supply. Kirchoff’s Voltage Law states that “the supply voltage in a closed circuit is equal to the sum of all the voltage drops (IR) around the circuit” and this can be used to good effect.

The Voltage Division Rule, allows us to use the effects of resistance proportionality to calculate the potential difference across each resistance regardless of the current flowing through the series circuit. A typical “voltage divider circuit” is shown below.

Voltage Divider Network

 

The circuit shown consists of just two resistors, R1 and R2 connected together in series across the supply voltage Vin. One side of the power supply voltage is connected to resistor, R1, and the voltage output, Vout is taken from across resistor R2. The value of this output voltage is given by the corresponding formula.

If more resistors are connected in series to the circuit then different voltages will appear across each resistor in turn with regards to their individual resistance R (Ohms Law IxR) values providing different but smaller voltage points from one single supply.

So if we had three or more resistances in the series chain, we can still use our now familiar potential divider formula to find the voltage drop across each one. Consider the circuit below.

The potential divider circuit above shows four resistances connected together is series. The voltage drop across points A and B can be calculated using the potential divider formula as follows:

We can also apply the same idea to a group of resistors in the series chain. For example if we wanted to find the voltage drop across both R2 and R3 together we would substitute their values in the top numerator of the formula and in this case the resulting answer would give us 5 volts (2V + 3V).

In this very simple example the voltages work out very neatly as the voltage drop across a resistor is proportional to the total resistance, and as the total resistance, (RT) in this example is equal to 100Ω or 100%, resistor R1 is 10% of RT, so 10% of the source voltage VS will appear across it, 20% ofVS across resistor R2, 30% across resistor R3, and 40% of the supply voltage VS across resistor R4. Application of Kirchoff’s voltage law (KVL) around the closed loop path confirms this.

Now lets suppose that we want to use our two resistor potential divider circuit above to produce a smaller voltage from a larger supply voltage to power an external electronic circuit. Suppose we have a 12V DC supply and our circuit which has an impedance of 50Ω requires only a 6V supply, half the voltage.

Connecting two equal value resistors, of say 50Ω each, together as a potential divider network across the 12V will do this very nicely until we connect the load circuit to the network. This is because the loading effect of resistor RL connected in parallel across R2 changes the ratio of the two series resistances altering their voltage drop and this is demonstrated below.

Resistors in Series Example No2

Calculate the voltage drops across X and Y.

a) Without RL connected

b) With RL connected

 

As you can see from above, the output voltage Vout without the load resistor connected gives us the required output voltage of 6V but the same output voltage at Vout when the load is connected drops to only 4V, (Resistors in Parallel).

Then we can see that a loaded voltage divider network changes its output voltage as a result of this loading effect, since the output voltage Vout is determined by the ratio of R1 to R2. However, as the load resistance, RL increases towards infinity (∞) this loading effect reduces and the voltage ratio ofVout/Vs becomes unaffected by the addition of the load on the output. Then the higher the load impedance the less is the loading effect on the output.

A variable resistor, potentiometer or pot as it is more commonly called, is a good example of a multi-resistor voltage divider within a single package as it can be thought of as thousands of mini-resistors in series. Here a fixed voltage is applied across the two outer fixed connections and the variable output voltage is taken from the wiper terminal. Multi-turn pots allow for a more accurate output voltage control.The effect of reducing a signal or voltage level is known asAttenuation so care must be taken when using a voltage divider network. This loading effect could be compensated for by using a potentiometer instead of fixed value resistors and adjusted accordingly. This method also compensates the potential divider for varying tolerances in the resistors construction.

The Voltage Divider Circuit is the simplest way of producing a lower voltage from a higher voltage, and is the basic operating mechanism of the potentiometer.

As well as being used to calculate a lower supply voltage, the voltage divider formula can also be used in the analysis of more complex resistive circuits containing both series and parallel branches. The voltage or potential divider formula can be used to determine the voltage drops around a closed DC network or as part of a various circuit analysis laws such as Kirchoff’s or Thevenin’s theorems.

Applications of Resistors in Series

We have seen that Resistors in Series can be used to produce different voltages across themselves and this type of resistor network is very useful for producing a voltage divider network. If we replace one of the resistors in the voltage divider circuit above with a Sensor such as a thermistor, light dependant resistor (LDR) or even a switch, we can convert an analogue quantity being sensed into a suitable electrical signal which is capable of being measured.

For example, the following thermistor circuit has a resistance of 10KΩ at 25°C and a resistance of100Ω at 100°C. Calculate the output voltage (Vout) for both temperatures.

Thermistor Circuit

 

At 25°C

 

At 100°C

 

So by changing the fixed 1KΩ resistor, R2 in our simple circuit above to a variable resistor or potentiometer, a particular output voltage set point can be obtained over a wider temperature range.

Resistors in Series Summary

So to summarise. When two or more resistors are connected together end-to-end in a single branch, the resistors are said to be connected together in series. Resistors in Series carry the same current, but the voltage drop across them is not the same as their individual resistance values will create different voltage drops across each resistor as determined by Ohm’s Law ( V = IxR ). Then series circuits are voltage dividers.

In a series resistor network the individual resistors add together to give the equivalent resistance, (RT ) of the series combination. The resistors in a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor or the circuit.

In the next tutorial about Resistors, we will look at connecting resistors together in parallel and show that the total resistance is the reciprocal sum of all the resistors added together and that the voltage is common to a parallel circuit.