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.