Electric Motor & Transformers

Fundamentals of Electric Motors and Transformers
Motors and transformers are the key driving force for industrial and residential appliances.We can’t even imagine an industry without motors and transformers. In industry all types of linear or rotational force, movement, torque, etc are applied by motors. Industries are getting automated day by day, hence the use of motors are increasing with the same pace. The power supply to any medium or large scale industry comes through transformer as the utilities prefer to supply at higher grid voltage. Maximum portion of power that is consumed in any industry is by motors. So the efficiency is a great issue for an industry owner to think about. The efficiency of the major consumer, the motor must be of as high as possible. The efficiency of the transformer, through which all the power is consumed, must also be near 100 percent. So every personnel related to the decision making in industry must have the knowledge regarding the energy efficiency issue for motors and transformers. 

Operation
To discuss about the operation of motors and transformers we must know the basic principles of Faraday’s Law of Electromagnetic induction. According to Faraday if there is any rate of change of flux incorporated inside a conducting loop then there will be an EMF, hence voltage induced in the loop. If the loop is shorted or connected end to end, then a current will flow through the conductor. The current will flow in such a direction so that the rate of change of flux created due to this current will try to nullify the rate of change of flux which is responsible for creating this current. This theory is the core of all machines. Transformer is a non-rotational device and motor is a rotational machine. Faraday’s law is equally applied to both of these machines. So we first need to know how we can apply the same theory to all the requirements in the industry and other household appliances. To explain the operation of transformer and motor we need to follow the following basics: 

Straight Conductor
Transformers and motors are all constructed by coils which are nothing but a wire or more scientifically we can say a conductor. If we apply AC voltages across a straight conductor shown in figure 1, then if the AC voltage source is capable of supplying sufficient current to burn the conductor, it is certain that the conductor will burn. Because it has a lower resistance and Ohm’s law will not hesitate to burn it! So the result is clear that the wire will burn within a second. Now the question is, what happens when a coil or an inductor, made with the same conductor, never burns with the AC source applied across it.

Inductor
An inductor is just a conductor which is twisted to make a coil. If we supply AC source across an inductor as shown in figure 2, it never burns. From Faraday’s law we know, if a rate of change of flux is cut through a loop of conductor then an EMF is induced across it. In case of inductor the applied AC source tries to flow an alternating current through it. Due to this alternating current an alternating flux is created inside the loop. This alternating flux will induce an EMF across the inductor. The more current will flow the more EMF will induce across it. But this induced voltage cannot exceed the applied voltage. So that amount of current will flow across the inductor which can induce the same amount of the applied voltage. This fact ascertains that the current will not increase to an abrupt value. As a result the inductor doesn't burn. 

Transformer
A transformer is an extended version of an inductor. The flux that is created inside the inductor is used here to induce voltages at other coil, which is termed as secondary coil. If the rate of change of flux can induce voltage across the primary coil, from which it is created, then it is also possible to induce voltage across secondary coil, provided that we can pull the flux to flow through the other coil. The rate of change of flux will induce voltage as many turn we use. If the turn is double the turn in primary then the voltage will also be double. If we increase the number of secondary coils, then voltage will be induced in all the secondary coils according to the number of turns present in each secondary coil. We can increase or decrease the secondary voltage level according to our requirement. If the secondary voltage is increased then it is called step up transformer and for the decreasing case it is called step down transformer. Each secondary voltage will act as a separate voltage source. Here the other advantage we get from a transformer is that each secondary voltage source is an isolated voltage source. There is no electrical connection between the primary and the secondary. Whatever voltage level is that, the secondary is totally an isolated part.

Motor 
A motor is an extended version of a transformer. Here we can introduce the analogy between a transformer and a motor that is a motor is like a transformer with a moving secondary. The primary that is not moving is called stator and the secondary that is moving is called rotor. The type of motor that is used worldwide with a greater percentage is the three phase induction motor.

The principle is somewhat like a transformer. If we place three coil at 120 degree physical alignment and also apply three phase ac supply which is also with 120 degree electrical phase relation, then the resultant flux, that is created from the vectorial space summation of the three phase fluxes, will rotate at the frequency of the supply voltage. Here the magnitude of the flux is same throughout the rotation. Now this revolving flux will cut the rotor and there will be an induced voltage across the rotor as well. As the rotor is short circuited there will be a flow of current through the short circuited loop. This current will create a flux which will interact with the revolving flux. There will be a force exerted upon this flux from the rotor. The current in the rotor will flow in such a direction so that it can decrease the rate of change of flux from which it is created. As a result the rotor will try to revolve in the direction of the revolving flux to reduce the rate of change of flux cut. When the rotor revolves then the relative velocity with the stator decrease and the rotor will rotate with a slip so that it can provide the necessary torque of the load. 

Types and Applications of Transformers 

Auto Transformers
An auto transformer has only a single winding with two end terminals, plus a third at an intermediate tap point. The primary voltage is applied across two of the terminals, and the secondary voltage taken from one of these and the third terminal. The primary and secondary circuits therefore have a number of winding turns in common. An adjustable auto transformer is made by the secondary connection through a sliding brush, giving a variable turns ratio. 

Poly Phase Transformers

For three-phase power, three separate single-phase transformers can be used, or all three phases can be connected to a single poly phase transformer. In this case, the magnetic circuits are connected together, the core thus containing a three-phase flow of flux. The three primary winding are connected together and the three secondary winding are connected together. The most common connections are Y-∆, ∆-Y, ∆-∆ and Y-Y. If a winding is connected to earth (grounded), the earth connection point is usually the center point of a Y winding. 

Leakage Transformers

A leakage transformer, also called a stray-field transformer, has a significantly higher leakage inductance than other transformers, sometimes increased by a magnetic bypass or shunt in its core between primary and secondary, which is sometimes adjustable with a set screw. This provides a transformer with an inherent current limitation due to the loose coupling between its primary and the secondary winding. The output and input currents are low enough to prevent thermal overload under all load conditions - even if the secondary is shorted. Leakage transformers are used for arc welding and high voltage discharge lamps. 

Resonant Transformers

A resonant transformer is a kind of the leakage transformer. It uses the leakage inductance of its secondary winding in combination with external capacitors, to create one or more resonant circuits. Resonant transformers such as the Tesla coil can generate very high voltages, and are able to provide much higher current than electrostatic high-voltage generation machines such as the Van de Graaff generator. 

Instrument Transformers

A current transformer is a measurement device designed to provide a current in its secondary coil proportional to the current flowing in its primary. Current transformers are commonly used in metering and protective relaying, where they facilitate the safe measurement of large currents. The current transformer isolates measurement and control circuitry from the high voltages typically present on the circuit being measured. Voltage transformers (VT) also referred to as potential transformers (PT) are used for metering and protection in high-voltage circuits. They are designed to present negligible load to the supply being measured and to have a precise voltage ratio to accurately step down high voltages so that metering and protective relay equipment can be operated at a lower potential. 

Zigzag Transformers

A zigzag transformer is a special purpose transformer. It has primary winding but no secondary winding.  One  application  is  to  derive  an  earth  reference  point  for  an un-grounded electrical system. Another is to control harmonic currents.

Pulse Transformers

A pulse transformer is a transformer that is optimized for transmitting rectangular electrical pulses (that is, pulses with fast rise and fall times and constant amplitude). Small versions called signal types are used in digital logic and telecommunications circuits, often for matching logic drivers to transmission lines. Medium-sized power versions are used in power-control circuits such as camera flash controllers. Larger power versions are used in the electrical power distribution industry to interface low-voltage control circuitry to the high-voltage gates of power semiconductors. Special high voltage pulse transformers are also used to generate high power pulses for radar, particle accelerators, or other high energy pulsed power applications. 

Speaker Transformers

In the same way that transformers are used to create high voltage power transmission circuits that minimize transmission losses, speaker transformers allow many individual loudspeakers to be powered from a single audio circuit operated at higher-than normal speaker voltages. This application is common in public address applications. Such circuits are commonly referred to as constant voltage or 70 volt speaker circuits although the audio waveform is obviously a constantly changing voltage. 

Isolation Transformers

An isolation transformer is a device that transfers energy from the alternating current (AC) supply to an electrical or electronic load. It isolates the winding to prevent transmitting certain types of harmonics.

Buck Boost Transformers

Buck Boost Transformers make small adjustments to the incoming voltage. They are often used to change voltage from 208 v to 240 v for lighting applications.  One major advantages of Buck boost transformers are their low cost, compact size and light weight. 

Pad Mounted Transformers

Pad Mounted Transformers are usually single phase or three phase and is used where safety is a main concern. Typical Application is restaurant, commercial building, shopping mall, institutional.

Pole Mounted Transformers

Pole Mounted Transformers are used for distribution in areas with overhead primary lines. Outside a typical house one can see one of these devices mounted on the top of an electrical pole.

Oil-filled transformers

Oil-filled transformers are transformers that use insulating oil as insulating materials.  The oil helps cool the transformer. Because it also provides part of the electrical insulation between internal live parts, transformer oil must remain stable at high temperatures over an extended period.

Dry type transformers

Dry type transformers require minimum maintenance to provide many years of reliable trouble free service. Unlike liquid fill transformers which are cooled with oil or fire resistant liquid dielectric, dry type units utilize only environmentally safe, CSA and UL recognized high temperature insulation systems. Dry type transformers provide a safe and reliable power source which does not require fire proof vaults, catch basins or the venting of toxic gasses. These important safety factors allow the installation of dry type transformers inside buildings close to the load, which improves overall system regulation and reduces costly secondary line losses.

Dry type transformers are a rather mature product and technology but, of all the components in a power system, a transformer replacement can be a physically challenging event, extended delivery of a replacement or repair unit and expensive transportation costs. These are transformers whose core and coils are not immersed in insulating oil. Fire-resistant dry type or "cast resin" transformers are well suited for installation in high rise buildings, hospitals, underground tunnels, school, steel factories, chemical plants and places where fire safety is a great concern. Hazard free to the environment, dry type transformers have over the years proven to be highly reliable.

“Dry type” simply means it is cooled by normal air ventilation. The dry type transformer does not require a liquid such as oil or silicone or any other liquid to cool the electrical core and coils.

Loss, Efficiency and Costing

Transformers reduce the voltage of the electricity supplied by the utility to a level suitable for use by the electric equipment. Since all of the electricity used by a company passes through a transformer, even a small efficiency improvement will result in significant electricity savings. High-efficiency transformers are now available that can reduce total electricity use by approximately 1 percent. Reduced electricity use provides cost savings for a company.

Two types of energy losses occur in transformers:Load Losses and No-Load Losses.

 Load Losses result from resistance in the copper or aluminum winding. Load losses (also called winding losses) vary with the square of the electrical current (or load) flowing through the winding. At low loads (e.g. under 30 percent loading), core losses account for the majority of losses, but as the load increases, winding losses quickly dominate and account for 50 to 90 percent of transformer losses at full load. Winding losses can be reduced through improved conductor design, including proper materials selection and increases in the amount of copper conductor employed.

No-Load Losses result from resistance in the transformer's laminated steel core. These losses (also called core losses) occur whenever a transformer is energized and remain essentially constant regardless of how much electric power is flowing through it. To reduce core losses, high-efficiency transformers are designed with a better grade of core steel and with thinner core lamination than standard-efficiency models.Total transformer losses are a combination of the core and winding losses. Unfortunately, some efforts to reduce winding losses increase core losses and vice verse. For example, increasing the amount of conductor used reduces the winding losses, but it may necessitate using a larger core, which would increase core losses. Manufacturers are developing techniques that optimize these losses based on the expected loading. 

Annual energy losses and cost of these losses

The annual energy losses of a transformer can be estimated from the following formula

W loss =8760(Po+Pk L)^2

Where,W _Loss - is the annual energy loss in kWh. 

P_o - is the no-load loss in kW.

P_k - is the short-circuit loss (or load loss) in kW. 

L - is the average per-unit load on the transformer. 

8760 - is the number of hours in a year.

To calculate the cost of these losses, they need to be converted to the moment of purchase by assigning capital values, to be able to put them into the same perspective as the purchase price. This is called the Total Capitalized Cost of the losses, TCC loss. This can be calculated using the formula 

Where

C - is the estimated average cost per kWh in each year.

 i - is the estimated interest rate.

n - is the expected life time of the transformer. 

Life Cycle Cost of Transformers

To perform the economical analysis of transformer, it is necessary to calculate its life cycle cost, sometimes called total cost of ownership, over the life span of transformer or, in other words, the capitalized cost of the transformer. All these terms mean the same - in one formula, costs of purchasing, operating and maintaining the transformer need to be compared taking into account the time value of money. The concept of the ‘time value of money’ is that a sum of money received today has a higher value - because it is available to be exploited - than a similar sum of money received at some future date. In practice, some simplification can be made. While each transformer will have its own purchase price and loss factors, other costs, such as installation, maintenance and decommissioning will be similar for similar technologies and can be eliminated from the calculation. Only when different technologies are compared e.g. air cooled dry type transformers with oil cooled transformers will these elements need to be taken into account. Taking only purchase price and the cost of losses into account the Total Cost of Ownership can be calculated

TCO = PP + APo+ BPk

Where, 

PP - is the purchase price of transformer,

A - represents the assigned cost of no-load losses per watt, 

P_o - is the rated no-load loss,

B - is the assigned cost of load losses per watt, 

P_k - is the rated load loss.

Types and Applications of Motors

Three Phase AC Induction Motors 

Where a poly  phase electrical supply is available, the three-phase (or poly phase) AC induction motor is commonly used, especially for higher-powered motors. The phase differences between the three phases of the poly phase electrical supply create a rotating electromagnetic field in the motor.Through electromagnetic induction, the time changing and reversing (alternating in direction poly phase currents) rotating magnetic field induces a time changing and reversing (alternating in direction)current in the conductors in the rotor; this sets up a time changing and counterbalancing moving electromagnetic field that causes the rotor to turn in the direction the field is rotating. The rotor always moves (rotates) slightly behind the phase peak of the primary magnetic field of the stator and is thus always moving slower than the rotating magnetic field produced by the poly phase electrical supply.

Induction motors are the workhorses of industry and motors up to about 500 kW (670 horsepower) in output are produced in highly standardized frame sizes, making them nearly completely interchangeable between manufacturers. Very large induction motors are capable of tens of thousands of kW in output, for pipeline compressors, wind-tunnel drives and overland conveyor systems.There are two types of rotors used in induction motors: squirrel cage rotors and wound rotors.

Squirrel cage rotor

Most common AC motors use the squirrel cage rotor, which will be found in virtually all domestic and light industrial alternating current motors. The squirrel cage takes its name from its shape - a ring at either end of the rotor, with bars connecting the rings running the length of the rotor. It is typically cast aluminum or copper poured between the iron laminates of the rotor, and usually only the end rings will be visible.

Wound rotor

An alternate design, called the wound rotor, is used when variable speed is required. In this case, the rotor has the same number of poles as the stator and the winding are made of wire, connected to slip rings on the shaft. Carbon brushes connect the slip rings to an external controller such as a variable resistor that allows changing the motor's slip rate.

Three Phase AC synchronous Motor

If connections to the rotor coils of a three-phase motor are taken out on slip-rings and fed a separate field current to create a continuous magnetic field (or if the rotor consists of a permanent magnet), the result is called a synchronous motor because the rotor will rotate synchronously with the rotating magnetic field produced by the poly phase electrical supply. The synchronous motor can also be used as an AC generator or alternator.One use for this type of motor is its use in a power factor correction scheme. They are referred to as synchronous condensers. This exploits a feature of the machine where it consumes power at a leading power factor when its rotor is over excited. It thus appears to the supply to be a capacitor, and could thus be used to correct the lagging power factor that is usually presented to the electric supply by inductive loads. The excitation is adjusted until a near unity power factor is obtained (often automatically). Machines used for this purpose are easily identified as they have no shaft extensions. Synchronous motors are valued in any case because their power factor is much better than that of induction motors, making them preferred for very high power applications. 

Two-phase AC servo motor

A typical two-phase AC servo motor has a squirrel-cage rotor and a field consisting of two winding a constant-voltage (AC) main winding and a control-voltage (AC) winding in quadrature with the main winding as to produce a rotating magnetic field. The electrical resistance of the rotor is made high intentionally so that the speed-torque curve is fairly linear.Two-phase servo motors are inherently high-speed-torque devices, heavily geared down to drive the load.

Single phase AC Induction Motor

Three-phase motors inherently produce a rotating magnetic field. However, when only single-phase power is available, the rotating magnetic field must be produced using other means. Several methods are commonly use. A common single-phase motor is the shaded-pole motor, which is used in devices requiring low starting torque, such as electric fans or other small household appliances. In this motor, small single-turn copper "shading coils" create the moving magnetic field. Another common single-phase AC motor is the split-phase induction motor, commonly used in major appliances such as washing machines and clothes dryers.Compared to the shaded pole motor, these motors can generally provide much greater starting torque by using a special start-up winding in conjunction with a centrifugal switch. Another variation is the permanent-split capacitor (PSC) motor (also known as a capacitor start and run motor). This motor operates similarly to the capacitor-start motor described above, but there is no centrifugal starting switch, and the start winding (second winding) are permanently connected to the power source (through a capacitor), along with the run winding. PSC motors are frequently used in air handlers, blowers, and fans (including ceiling fans) and other cases where a variable speed is desired. 

Repulsion motors

Repulsion motors are wound-rotor single-phase AC motors that are similar to universal motors. In a repulsion motor, the armature brushes are shorted together rather than connected in series with the field.

Single Phase AC Synchronous Motors

Small single-phase AC motors can also be designed with magnetized rotors (or several variations on that idea). The rotors in these motors do not require any induced current so they do not slip backward against the mains frequency. Instead, they rotate synchronously with the mains frequency. Because of their highly accurate speed, such motors are usually used to power mechanical clocks, audio turntables, and tape drives; formerly they were also much used in accurate timing instruments such as strip-chart recorders or telescope drive mechanisms. The shaded-pole synchronous motor is one version.

Brushed DC Electric Motor

A brushed DC motor is an internally commutated electric motor designed to be run from a DC power source.

Reluctance Motor
A reluctance motor is a type of synchronous electric motor which induces non-permanent magnetic poles on the ferromagnetic rotor. Torque is generated through the phenomenon of magnetic reluctance. A reluctance motor, in its various incarnations, may be known as a: 

• Synchronous Reluctance motor
• Variable Reluctance motor 
• Switched Reluctance motor (SRM)
• Variable Reluctance Stepping motor 

SRM's are used in some washing machine designs. SRM's are commonly used in the control rod drive mechanisms of nuclear reactors.

Uni-Polar Motor

A Uni-Polar motor is a type of small DC electric motor commonly found in small, portable cassette players. Its name is derived from its construction, which employs a magnetic strip wrapped around the inner wall of the housing such that one of its poles faces the inside, while the other faces outward. 

Linear Motor

A linear motor or linear induction motor is essentially a multiphase alternating current electric motor that has had its stator "unrolled" so that instead of producing a torque it produces a linear force along its length. When a linear motor is used to accelerate beams of ions or subatomic particles, it is called a particle accelerator. The design is usually rather different as the particles move close to the speed of light and are generally electrically charged.  

Brush less DC Electric Motor

A Brush less DC motor (BLDC) is a synchronous electric motor which is powered by direct-current electricity (DC) and which has an electronically controlled commutation system, instead of a mechanical commutation system based on brushes. In such motors, current and torque, voltage and rpm are linearly related. BLDC motors can potentially be deployed in any area currently fulfilled by brushed DC motors. Cost and control complexity prevents BLDC motors from replacing brushed motors in most common areas of use. Nevertheless, BLDC motors have come to dominate many applications: Consumer devices such as computer hard drives, CD/DVD players, and PC cooling fans use BLDC motors almost exclusively. Low speed, low power brush less DC motors are used in direct-drive turntables. High power BLDC motors are found in electric vehicles and some industrial  machinery.  These  motors  are  essentially  AC  synchronous  motors  with permanent magnet rotors. 

Stepper Motor

A stepper motor (or step motor) is a brush less, synchronous electric motor that can divide a full rotation into a large number of steps. Computer-controlled stepper motors are one of the most versatile forms of positioning systems. They are typically digitally controlled as part of an open loop system, and are simpler and more rugged than closed loop servo systems.Industrial applications are in high speed pick and place equipment and multiaxis machine CNC machines often directly driving lead screws or ball screws. In the field of lasers and optics they are frequently used in precision positioning equipment such as linear actuators, linear stages, rotation stages, goniometers, and mirror mounts. Other uses are in packaging machinery, and positioning of valve pilot stages for fluid control systems Commercially, stepper motors are used in floppy disk drives, flatbed scanners, computer printers, plotters and many more devices.

Step 1 : Know the Load Characteristics

For line-operated motors, loads fall into three general categories: constant torque, torque that changes abruptly, and torque that change gradually over time.Bulk material conveyors, extrudes  positive displacement pumps, and compressors without air loaders run at relatively steady levels of torque. Sizing a motor for these applications is simple once the torque (or horsepower) for the application is known. Load demands by elevators, compactors, punch presses, saws, and batch conveyors change abruptly from low to high in a short time, often in a fraction of a second. The most critical consideration for selecting a motor in these cases is to choose one whose speed-torque curve exceeds the load torque curve.Loads from centrifugal pumps, fans, blowers, compressors with unloaded, and similar equipment tend to be variable over time. In choosing a motor for these conditions, consider the highest continuous load point, which typically occurs at the highest speed. 

Step 2 : Get handle on Horse Power

The rule of thumb for motor horsepower is: Select only what you need, and avoid the temptation to oversize or under size. Calculate the required horsepower from this formula:

                                     

                                          Horsepower =   Torque x Speed / 5250

Where torque is in lb-ft and speed is in rpm. 

Step 3 : Getting Started

Another consideration is inertia, particularly during start up. Every load represents some value of inertia, but punch presses, ball mills, crushers, gearboxes that drive large rolls, and certain types of pumps require high starting torques due to the huge mass of the rotating elements. Motors for these applications need to have special ratings so that the temperature rise at start up does not exceed the allowable temperature limit. A properly sized motor must be able to turn the load from a dead stop (locked-rotor torque), pull it up to operating speed (pull-up torque), and then maintain the operating speed. Motors are rated as one of four “design types” for their ability to endure the heat of that starting and pull up. In ascending order of their ability to start inertial loads, NEMA designates these as design type A, B, C, and D. Type B is the industry standard and is a good choice for most commercial and industrial applications. 

Step 4: Adjust for duty cycle 

Duty cycle is the load that a motor must handle over the period when it starts, runs, and stops.

Continuous duty is by far the simplest and most efficient application. The duty cycle begins with start up, then long periods of steady operation where the heat in the motor can stabilize as it runs.  A motor in continuous duty can be operated safely at or near its rated capacity because the temperature has a chance to stabilize.

Intermittent duty is more complicated. The life of commercial airplanes is measured by their number of landings; in the same way, the life of a motor is proportional to the number of starts it makes. Frequent starts shorten life because inrush current at start up heats the conductor rapidly. Because of this heat, motors have a limited number of starts and stops that they can make in an hour.

Step 5 : The Last Consideration, Motor Hypoxia 

If your motor is going to operate at altitudes that are substantially above sea level, then it will be unable to operate at its full service factor because, at altitude, air is less dense and does not cool as well. Thus, for the motor to stay within safe limits of temperature rise, it must be de-rated on a sliding scale. Up to an altitude of 3,300 ft, SF = 1.15; at 9000 ft, it declines to 1.00. This is an important consideration for mining elevators, conveyors, blowers, and other equipment that operates at high altitudes.\

Should You Buy New or Rewind?

When you have a motor failure you’ll need to decide if you should buy a new motor or fix the old one. A common cause of motor failure is problems with the motor winding, and the solution often is to rewind the old motor. Because it is economical in terms of initial cost, rewinding of motors is very common particularly for motors of more than 10 horsepower. However, the motor rewinding process often results in a loss of motor efficiency. It is generally cost-effective to replace motors under 10 horsepower with new high-efficiency motors rather than rewind them. When deciding whether to buy a new motor or rewind the old one, consider the cost difference between the rewind and a new high-efficiency motor, and the potential increase in energy costs of a rewound motor that is less efficient than the original. The quality of the rewind as a big impact on operating cost. A poorly rewound motor may lose up to 3% in efficiency. A 100 HP motor may use several hundred dollars more in electricity each year due to this drop in efficiency, compared to its original efficiency. The operating cost may be even more compared to a new high efficiency motor. 

Fundamentals of Electricity..2

SERIES CIRCUITS

When all the parts of a circuit are electrically connected end to end, they are said to be in series.The current flows from the battery E through the resistor R1, then through the resistor R2, and returns to the battery E. 

The total resistance of a series circuit is equal to the sum of the individual resistances. If R1 and R2 are the series resistors, then their total resistance is: R= R1 + R2. 

Thus, if R1 is 5 ohms and R2 is 10 ohms then:R = 10 + 5 = 15 ohms

There are three fundamental laws that apply to any series circuit. These laws are:

• In a series circuit, the same current flows through each component in the circuit.
• In a series circuit, the total resistance is the sum of the individual resistance's making up the circuit.
• In a series circuit, the applied voltage is equal to the sum of the individual voltage drops.

PARALLEL CIRCUITS

When two or more electrical devices are connected so that each one offers a separate path for the flow of the current between two points, the devices are said to be in parallel. In the figure below, the two resistors R, and R2 are shown connected in parallel.

The total current set up by the battery divides at point A, a part going through the resistor R₁ while the other part flows through the resistor R₂. At the junction point of B, the two currents unite and return to the battery. The resistor R₂ is in parallel with resistor R₁.  Similarly, the resistor R₁ is in parallel with resistor R₂.

The two branch circuits consisting of the resistors R₁ and R₂ form two separate paths in parallel. An open circuit in either branch will not stop the flow of current through the other branch, because each branch forms a separate and complete path from point A to point B. An open circuit in the main conductors, between point A or B and the battery, would interrupt the current in the entire circuit.

The total current in a parallel circuit is the sum of the currents in each branch. Since each branch is connected directly to the battery, the current in it is calculated according to Ohms Law. If the battery voltage E is 30 V and R₁ is 5 ohms, then the current in R₁ is E / R₁ or 30 / 5 = 6 amps. If R₂ is 10 ohms, the current in it is 30 / 10 = 3 amps. The total current is the summation of the branch currents, or I₁ + 1₂ = I_T .  Thus 6 + 3 = 9.

Since the combined current in the two parallel resistors is 9 amps and the voltage is 30, according to Ohms Law the two resistors in parallel must have a resistance R_T = E / I = 30 / 9 = 3 1/3 ohms, which is less than the resistance of either resistor.

Laws for Parallel Circuits

The facts pointed out concerning parallel circuits may   be   summarized   in   the   form   of   three fundamental laws which will apply to any parallel circuit. These laws are:

• In a parallel circuit, the same voltage is applied to each individual branch.
• In a parallel circuit, the total current is equal to the sum of the currents in the individual branches.
• In a parallel circuit, the effective resistance is equal to the applied voltage divided by the total current, and this value is always less than the smallest resistance contained in the circuit.

Unit of Resistivity

From what has been discussed regarding series circuits, it would be a reasonable conclusion to say that the resistance of a conductor increases as its length increases. By the same token, from what has been said regarding parallel circuits, the resistance of a conductor must decrease as its cross-sectional area increases. 

Experiments have proven this true, and it is found that the resistance is proportional to the length and that the resistance is inversely proportional to the cross-sectional area.

To mathematically relate these for any conductor, we must introduce proportionality constant, called Resistivity whose symbol is the Greek letter ρ (rho). Combining all of these factors, we can express the resistance of any conductor by, R=ρL/A or ρ=RA/L

Since R is in ohms, and if A is in square centimeters (cm^2), and L is in centimeters (cm), then:

ρ=ohms x cm^2/cm=ohm-cm

Thus  ρ,  that  is,  Resistivity  has  the  dimension ohm-centimeter.  Resistivity then is equal to the resistance of a conductor which is 1 centimeter long with a constant cross-sectional area of 1 square centimeter.

ELECTRICAL INSTRUMENTS 

Meter Movement Sensitivity and Accuracy

The sensitivity of a meter movement depends upon the amount of current necessary to operate the moving element of the meter. The meter movement requiring the least amount of current for full scale deflection is considered to be the most sensitive. 

The amount of current necessary for full scale deflection depends upon the number of turns of wire on the moving coil. When more turns are added, a stronger magnetic field is created; thus, less current is necessary for full scale deflection.

Ammeters

The ammeter is the instrument used to indicate the quantity of current in an electrical circuit. In order to measure the amount of current in a circuit, the ammeter must be placed in series with the circuit. The figure below shows a DC ammeter connected into an electrical circuit.

The  two  resistors,  R  and  RV,  represent  the resistance of the ammeter and the over-all circuit, respectively. When the ammeter is manufactured, the resistance RA is kept as small as possible so that the value current indicated by the movement will be close to the actual circuit current when the ammeter is removed. Note that the ammeter has polarized terminals to indicate proper circuit connection of the ammeter.

The ammeter shown in the figure above has the disadvantage of being able to indicate only one range of current. To measure higher values of direct current,  the  meter  may  incorporate  a  suitable resistor called a meter shunt connected in parallel with the meter movement as shown in the below figure. 

For full scale deflection of the meter pointer, the meter shunt provides a path for the portion of the current in excess of that required by the sensitivity of the meter movement. Assume that the movement sensitivity of the meter in the above figure is one ampere. With the addition of the proper shunt resistance, the ammeter circuit allows a total of 5 amperes to pass before the pointer indicates full-scale deflection -- 4 amperes through the shunt and 1 ampere through the movement; therefore, the maximum current reading ability of the ammeter has been increased by the addition of the shunt resistor. 

Determination   of   the   correct   value   of   shunt resistances  for  different  meter  movements  and current ranges can be accomplished by using Ohms Law as applied to parallel circuits. The following illustrates a typical problem in the calculation of a meter shunt. The meter movement shown below has a   full-scale   deflection   sensitivity   of   one milliampere.  It is desired to connect a shunt resistor to increase the current indicating capability of the movement to ten milliamperes. Since the movement can  safely  handle  only  one  milliampere,  nine milliamperes must flow through the shunt.

Expressing the current through the shunt resistance in terms of commonly used symbols provides the following relationship:

I_s = I_t - I_m

where:

I_s = current through the shunt
I_t = total current to be measured

I_m = current through the meter

Since the internal resistance of the meter is shown to be 45 ohms, the shunt must have one-ninth of this resistance or a resistance of 5 ohms to carry the required current.

To prove the above statement, the following should be considered. Knowing that the current through the meter movement is one milli-ampere (I_m) and its resistance is 45 ohms (R_m), the voltage drop across the meter can be calculated by Ohms Law.

E_m = I_m x R_m
E_m = 0.001 x 45
E_m = 0.045 volt

Since  the  voltage  across  the  network  (meter movement and shunt) is known, further application of   Ohms   Law   will   provide   the   resistance requirement of the shunt.

R_S = E_S/I_S

R_S = 0.045/0.009 

R_S = 5 ohms

Through  mathematical  substitution,  a  standard formula can be established for determining the required resistance of any meter shunt, providing the  current  through  the  shunt  is  known.  The standard formula is:

 R = (I_m x R_m)/I_s

Effect of Ammeter Resistance on Circuit Resistance

When an ammeter is inserted in an electrical circuit, it increases the effective circuit resistance. This will reduce the current flow in the circuit in accordance with Ohm's Law.

The  practical  effect  may  or  may  not  be  a consideration depending upon the relative values of the  original  circuit  resistance  and  the  inserted ammeter   resistance.   The   ammeter   should,   in general, ever have a resistance that is greater that 1% of the circuit resistance into which it is being inserted.

Voltmeters

The voltmeter is the instrument used to indicate the quantity of voltage present in an electrical circuit. In order to correctly measure the voltage of a circuit or circuit component, the voltmeter must be placed in parallel with the circuit. A DC voltmeter is capable of measuring only DC voltages, since the current must  pass  through  the  meter  movement  in  a specified direction.

The following figure shows the internal components of a voltmeter (enclosed in dotted lines), which is connected as a unit to a circuit for the measurement of  voltage.  Note  that  the  voltmeter  circuit  is composed of an ammeter in series with a resistor (Rm). The resistance, Rm, is a high-value resistance placed in series with the meter movement resistance to reduce the amount of current flowing through the movement.

As illustrated, when the voltmeter is placed across the circuit component, R1, the current flowing through the voltmeter causes a deflection of the meter needle. The resistance, Rm, is called the multiplier resistance because, if its ohmic value is increased, the same current would still be required to   cause   full-scale   deflection   of   the   meter movement, but more voltage would be required to cause this current to flow.

If we experimentally set up the circuit as shown in the figure below we can determine the resistance of the coil assuming that the required current is 1 milli-ampere for full scale deflection.

By adjusting the variable resistor until the meter reads full scale (.001 ampere), we know that the total circuit resistance (meter plus resistor value) must be 1000 ohms. Assume that the variable resistor was measured and found to be 950 ohms, then the meter coil itself must be only 50 ohms. Thus, the basic instrument has a 50 milli-volt drop movement.

E = IR = 0.001*50 = .050volts

From this we have seen that in order to use this basic instrument as a voltmeter, we had to add series  resistance.  In  this  case  the  total  circuit resistance is 1000 ohms. Thus, by definition, this instrument, when used as a voltmeter, would have a sensitivity of 1000 ohms per volt.

                 

              R = E/I = 1/0.001 = 1000 ohms

Normally, sensitivity is expressed in the fashion --ohms per volt. Thus, when you read on the face of a meter its sensitivity, you can, of course, determine the current required for full scale deflection, but you do not know the basic movement resistance.

From the case illustrated, it is obvious that in order to use any meter as a voltmeter, it is necessary that the internal resistance be known. We can then produce a voltmeter to read any voltage utilizing a basic formula.

E = I_m x R_m + I_m x R_s 

where:

I_m = meter current 

R_m = meter resistance 

R_s = series resistance 

E = desired voltage range:

 R_s = E_m/I_m - R_m

Then to produce a 100 volt full range instrument with  the  basic  movement  that  has 50  ohms resistance   and 0.001   ampere   sensitivity,   the necessary series resistor is:R_s = 100/0.001 - 50 = 99,950 ohms The  series  resistors  required  for  the  voltmeter ranges are known as multiplier resistors.Suppose that it is desired to know the voltage appearing across the load in the figure below.

Now we know from the circuit values given that a current of .001 ampere must be flowing in the circuit. The voltage drop appearing across the 10 K ohm load resistor must be 10 volts. Now, if a 1000 ohm per volt meter with a full scale of 10 volts (that is a total resistance of 10 K) were placed in parallel with load, parallel resistance of the load and meter must be 5 K.

The circuit resistance then is  95 K, and the total current per Ohms Law (100 volts / 95,000 ohms) must be .001053 ampere. The voltage as read by the meter then must be:

E = .001053 x 5000 = 5.263 volts

From the circuit conditions set up, we know it should have read 10 volts. Therefore, the voltmeter itself has introduced a large magnitude of error, and in terms of percent this is:

% error = [1 - (observed voltage/true voltage)] x 100% % error = [(1 - (5.26/10)] x 100% = 47.4%

We can draw two conclusions from the explanation above.

• Any voltmeter, since it is a current-operated device, will introduce an error.
• To minimize error, the sensitivity of the meter must be high.  That is, the smaller the current, the more accurate the reading will be.

THE DIGITAL DIRECT CURRENT INSTRUMENT

Digital   instruments   are   a   relatively   recent innovation  as  compared  to  the  moving  needle analog instruments. They have many advantages making them particularly useful to the corrosion control worker on underground structures. There are also some disadvantages. The development and improvement of such instruments is a continuing thing with new advances in electronic technology. The corrosion worker will do well to keep abreast of such developments to assure himself that he is equipped with the best available equipment for his purposes.

Operating Principles

The figure below is a representation of a digital instrument for the purpose of illustrating some of the pertinent points concerning such devices. No attempt is made to diagram the electronic circuitry the details of which can be quite complex and which can vary with the instrument manufacturer.

Whereas the analog instruments described earlier have mechanically moving parts, a digital readout instrument is entirely electronic with no moving parts. Although the figures in the digital readout module  may  appear  to  move  as  the  indicated reading  changes,  this  is  simply  the  changing formation of the digital characters as the applied electrical signal changes. There is no actual physical movement.

There are two types of digital readout modules. One of   these   utilizes   LED (light   emitting   diode) elements to form the characters in the readout. As the name implies, when such a diode is energized by an electrical signal, it shows up as bars of light.

The other type of readout utilizes LCD  (liquid crystal diode) elements. Such a diode is normally a neutral light color because it reflects light, but when energized by an electrical signal, it appears as a dark bar (absorbs light) which contrasts with the light  background  color.  Of  the  two  types,  the liquefied  crystal  readouts  are normally used  in corrosion test instruments for field use since they take less energy from the instrument batteries and can be easily read in bright sunlight. The discussion herein  assumes  that  liquefied  crystal  readout displays will be used.

One of the more important differences between the analog instruments described earlier and a digital instrument is the fact that all the energy needed to operate a moving coil analog instrument has to come   from   the   external   circuit   in   which measurements   are   being   made.   The   digital instrument, on the other hand, takes very little energy from the external circuit. The energy needed to operate its circuitry comes from internal long-life batteries in these electronic instruments.

When the digital instrument is used as a voltmeter, the  unknown  input  voltage  at  the  instrument terminals bypasses the ammeter shunt module and is applied to the DC amplifier module. Here the applied voltage encounters a high input resistance --typically ten million ohms or higher. This will be a fixed value which will be the same regardless of the voltage readout range selected. This very high input
resistance means that the current taken from the external circuit will be very small and thus the reading  will  be  more  accurate.  Although,  as indicated, the input resistance normally remains constant for all voltage ranges, there are some digital instruments for corrosion work which have a provision for changing the input resistance  (by pressing a button or rotating a selector switch) in order to see if the reading remains essentially the same with both values of input resistance. If they are the same, this indicates that external circuit resistance is not a problem. If there is a difference between the two readings, interpretive techniques may be used to arrive at the true potential.

The direct current amplifier, as its name implies, amplifies the input signal to a value that will actuate the readout module after adjustment using the range selector module.

In addition to the numerical figures (or digits) in the readout module, the decimal point will appear in its correct location for the range that has been selected. 

If the voltage being measured has been incorrectly connected to the instrument (+) to (-) and (-) to (+) instead of (+) to (+) and (-) to (-) as it should be, or if the polarity of the input voltage changes, a (-) sign will normally appear on the readout panel. Depending on the manufacturer, other information may appear as well, such as a low battery indicator when instrument batteries need replacement. There may also be an indication to show if an applied voltage or current is beyond the range selected.

When the instrument is used in the ammeter mode, shunt resistors are used for various current ranges as has been described earlier for analog instruments. The voltage drop across the shunts is then applied to the   electronic   circuitry   as   described   for   the voltmeter mode with the measured value appearing on the readout module. An important difference from the analog ammeter described earlier is that less energy is taken from the external circuit since most of the instrument operating energy comes from its internal batteries. Since shunts are used for the ammeter mode, the discussion relating to the effect of the shunt resistances on the external circuit is generally similar to that discussed under analog instruments.

Accuracy

Digital instruments, being non-mechanical, can be made with greater accuracy than analog instruments in the same price bracket. Normally, the accuracy of a digital instrument is expressed differently from that of an analog instrument as discussed earlier. This may be expressed, for example, as ± (plus or minus) a percentage of the actual reading, ± a percentage of the full scale reading, ± one digit in the last place (right hand figure) of the indicated readout. The net percentage accuracy figures can be quite high (depending on manufacturer and quality) as compared with analog instruments.

Advantages

Some  of  the  advantages  of  digital  instruments compared with analog instruments are as follows. 

• High input resistance to electronic circuit with  very  little  energy  taken  from  the external circuit in which measurements are being taken.
• High accuracy.
• Decimal point shown in correct location, thus reducing possibility of human error.
• No   interpretation   of   needle   position necessary   between   divisions (as   often required   with   analog   instruments)   thus further reducing the possibility of human error.
• No polarity problem  -- instrument reads correctly regardless of polarity as long as the reversed polarity indicator (negative sign) is observed.
• Relatively rugged for field use.

Disadvantages

Nothing is perfect. There are some disadvantages with respect to digital instruments although certain of  these  are  subject  to  improvement.  Typical disadvantages are as follows:

• Taking readings under dim light conditions where   liquid   crystal   readouts   may   be relatively difficult to see.
• Certain   components   of   the   electronic circuitry  may  have  a  narrower  operable  temperature range than analog instruments. 
• Liquid crystal read-out panels tend to be sluggish at low temperatures and tend to blank out if the temperature is too high. In extreme cases, the readout panel can be permanently    damaged    by    excessive temperature.
• Reading  continuously  varying  values.  In some  types  of  corrosion  control  work, voltages and currents being measured may be subject to continuous variation rather than being a steady value. Stray current situations are an example. In such situations, the digital readout panel can be a confusing display  of  continuously  changing  digits making it difficult to determine or estimate, maximum, minimum and average figures. Although still difficult, this can be more readily done with an analog instrument.
• In order to get the advantages of electronic circuitry and still permit an analog readout, hybrid instruments are available which use the electronic circuitry to operate an analog readout. Such   instruments   retain   the advantage  of  minimal  operating  energy taken from the external circuit since the energy needed to operate the analog readout is  provided  by  the  instrument  internal batteries.

COMBINATION INSTRUMENTS

For use in corrosion control work, combination instruments have been developed which, typically, have       two indicating instruments with interconnecting  circuitry  and  selector  switches. These   are   so   arranged that various testing requirements  may  be  set  up  by  proper  switch settings. This reduces the wiring as compared to that needed for separate instruments. Time needed to  set  up  for  a  particular  test  is  reduced  and possibilities of wiring errors are reduced. Additionally, single-instrument  multi-testers  are available (both analog and digital) which measure both DC voltage and current as has been discussed. but in addition can measure AC voltage and (in some  instances)  AC  current  and  can  measure resistance. Such instruments are a great convenience to the underground corrosion control worker.

CLAMP-ON INSTRUMENTS

A specialized type of instrument is available which is  useful  for  measuring  currents  in  conductors where it is desired to do so without interrupting the circuit.  These  are  called  clamp-on  instruments. These typically incorporate a split or hinged ring of magnetic core material which is clamped around the conductor in which current is to be measured.

Clamp-on instruments are available to measure both AC current and DC current. The sensing device may differ between the two types. Instruments designed for AC current measurement can measure an induced voltage in a coil surrounding the ring at one   point   with   the   induced   voltage   being proportional to the amount of current flow through the conductor. The instrument designed for DC current   measurement   electronically   senses   the distortion in the magnetic field in the clamp-on ring caused by the continuous mono-directional current flow.

Both types of instruments are available to cover a wide range of full scale current.At least one maker of DC clamp-on instruments can supply clamp-on rings in various diameters from smaller sizes for wires or cables to large rings that can surround pipes.

COMPUTER-COMPATIBLE INSTRUMENTS

With  the  continuing  development  of  computer usage,  the  appearance  of  computer-compatible field-testing instruments was inevitable.  Typically, this is an adjunct to electronic testing instruments that permits the corrosion worker to store recorded data on command in some form of internal storage device (RAM, ROM, tape, disc, etc.) incorporated in the instrument. Numerical measurements can be supplemented with coded information as to location and type of test plus supplementary information appropriate to the test being made.  This data can also normally be recorded and then downloaded into a PC computer for more detailed analysis while in the field Storing information in the above fashion reduces field time in data taking. The stored information can also be later transferred to a desktop computer that can be used to record, analyze and process the data in accord with record keeping programs that have been   developed   for   the   operating   company's purpose.