Wheatstone bridge

Wheatstone bridge is a measuring instrument invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. This is used to measure an unknown electrical resistance by balancing two legs of the bridge, one leg that includes the components known. it works similar to the original potentiometer.

Basic law of electric circuits associated with the Wheatstone bridge:

1. Ohm's Law
Ohm's Law states "If an electric current through a conductive, the current strength is proportional to the voltage-larus contained between the two ends of Conductor earlier."

This law was coined by Georg Simon Ohm, a physicist from Germany in 1825 and published in a paper entitled The Galvanic Circuit Investigated Mathematically in 1827.


The formula for Ohm's Law

Mathematically, Ohm's law is written

V = I.R
or
I = V / R

where
I = electric current that flows in a Conductor (Ampere)
V = voltage found on both ends of the Conductor (Volt)
R = electrical resistance found in a Conductor (Ohm)

2. Kirchoff Law I
Mid-19th century, Gustav Robert Kichoff (1824-1887) found a way to determine the electric current in the circuit branch which became known to the law of Kirchoff. Kirchoff law reads "The number of strong currents that enter the branching point equal to the amount of flow coming out strong from the point of branching."

The number I enter = I out

3. Kirchoff Law II
Kirchoff Law II reads, "In a closed circuit, the algebraic sum emf (E) and total potential drop equal to zero."

Purpose of the total potential drop equal to zero is the absence of electrical energy is lost in the circuit or in the sense that all energy can be used or absorbed.

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Radiation Polymerization

The use of irradiation technology is big enough in the process of an industrial chemical. Because it brings high energy, radiation may act as a catalyst to stimulate the chemical changes suatuÆÒhan, one of which is to change the type of liquid chemicals from organic compounds in the class of monomers into polymers. One of these is the nature of the monomer when receiving radiation exposure can be turned into new materials called polymers, which is a very hard solid material at room temperature. Polymer-making technique with the help of this radiation is called radiation polymerization. In industry, radiation polymerization technology can be used to produce high-quality plastic because of its very strong and resistant to heat.

In general it can be said that the polymerization is an effort to combine several elements into one cohesive substance. Utilization of the results of irradiation in the polymer industry the most is for the manufacture of electric cable insulation material. Irradiation causes long-chain molecules in polymers holding in certain places that the process known as crosslinking (crosslinking). Radiation energy can stimulate the occurrence of crosslinking between the polymer thus formed three-dimensional network that can change the properties of polymers. These events actually cause cable insulation materials are more resistant to heat and high voltage electricity.

Conductor metals currently used for power transmission cables are still a prisoner-in, thereby causing electric current dialirkannya partly converted into heat which is known as Joule heating. The higher the temperature, the higher the resistance-in, so that more electrical energy converted into heat dialirkannya. Because of Joule heating, too, the strong currents flowing in the cable should be limited. That is why, certain electronic goods, computers for example, equipped with a fan to remove heat that occurs in the circuit-circuit.

PVC plastic is made of polymer material can maintain the density of the irradiation at much higher temperatures than ordinary PVC (the result of chemical processes). With this irradiation technology, cable insulation materials become stronger, more elastic, and more resistant to oils and other chemical solutions. This advantage can be achieved without causing changes in electrical properties as well as insulating power.

Irradiation technology can also modify polyethylene polymer product can be shrunk if the volume is given a heat treatment which is often referred to as heat shrinkable tubes. This product is widely used in the electric industry to insulate electrical connections. Heat shrinkable tubes are also often used in the telecommunications industry for the packing units such as cable telephone cable unit, to be shielded from outside influences, more durable, safe and can be planted in the ground.

Irradiation technology is very efficient and economical to manufacture polymeric small-diameter cable insulation material that is widely used in electronics industry which requires high accuracy, such as computers and telecommunications aircraft. For some types of electronics products, the use of high quality cable is often a necessary condition, so our product really can be reliable and competitive.

Very thin surface layer (membrane) on a silver oxide batteries used in digital watches and calculators, as well as the surface of the floppy disks and tape record the video tape, are processed using irradiation technology. Researchers from Japan have succeeded in making polymer membranes of cellulose that is used for microphone or a magnifying system of acoustic sound. This high-quality membranes are being developed for the manufacture of commercial sound systems and high-quality musical instruments. In the field of energy, solid polymer electrolyte (solid polymer electrolyte) can be used to manufacture chemical fotoelektro cells. These polymers are made from polyethylene oxide (PEO) that is coupled with potassium jodida (KJ) and jodium (J2). Research in this field still continues to be developed to obtain a system of solid polymer electrolyte which would later be used as batteries for solar electric generating systems (solar energy).

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AC Generation

An understanding of how an AC generator develops an AC output will help us analyze the AC power generation process.

The elementary AC generator (Figure 1) consists of a conductor, or loop of wire in a magnetic field that is produced by an electromagnet. The two ends of the loop are connected to slip rings, and they are in contact with two brushes. When the loop rotates it cuts magnetic lines of force, first in one direction and then the other.

Development of a Sine-Wave Output

Figure 1 Simple AC Generator

At the instant the loop is in the vertical position (Figure 2, 0o), the coil sides are moving parallel to the field and do not cut magnetic lines of force. In this instant, there is no voltage induced in the loop. As the coil rotates in a counter-clockwise direction, the coil sides will cut the magnetic lines of force in opposite directions. The direction of the induced voltages depends on the direction of movement of the coil. The induced voltages add in series, making slip ring X (Figure 1) positive (+) and slip ring Y (Figure 1) negative (-). The potential across resistor R will cause a current to flow from Y to X through the resistor. This current will increase until it reaches a maximum value when the coil is horizontal to the magnetic lines of force (Figure 2, 90o). The horizontal coil is moving perpendicular to the field and is cutting the greatest number of magnetic lines of force. As the coil continues to turn, the voltage and current induced decrease until they reach zero, where the coil is again in the vertical position (Figure 2, 180o). In the other half revolution, an equal voltage is produced except that the polarity is reversed (Figure 2, 270o, 360o). The current flow through R is now from X to Y (Figure 1).

The periodic reversal of polarity results in the generation of a voltage, as shown in Figure 2. The rotation of the coil through 360° results in an AC sine wave output.

Summary

• A simple generator consists of a conductor loop turning in a magnetic field, cutting across the magnetic lines of force.
• The sine wave output is the result of one side of the generator loop cutting linesof force. In the first half turn of rotation this produces a positive current and in the second half of rotation produces a negative current. This completes one cycle of AC generation.

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Phasor analysis, power factor, and the calculation of 3-phase

Fasor sinusoid wave
In the field of electronics, bearan-scale current and voltage can be calculated by measuring because these quantities do exist and manifest in a series. But in the calculations are often settled by way of abstraction because in addition to simplify calculations, the concept of abstraction phasor important in electronics education. Phasor state transformation of a function of time into a complex field that contains information about the amplitude and phase angle.

Analysis of the spin vector at specified intervals called phasor analysis which, if associated with sine wave form will allow the depiction of phasor sinusoids are very important in an electronic problem.

1. There are many phenomena in nature which can be described as a sinusoidal wave.
2. Because of easy pembangktannya, then the current and voltage in the power generation shaped sinus.
3. Appropriate description of Fourier series, all other periodic waves, with certain conditions can be decomposed into the sum of sine waves with varying frequency.
   In a linear circuit consisting of resistance (R), inductor (L) and capacitor (C), if a current or voltage is a sinusoid, then semuja currents and other teganagan dengaan sinusoids also shaped the same frequency.

Through the Kirchoff law there are 3 ways to addition and subtraction sinusoids forms:

1. Graphical way, by describing the wave after wave and added all the time. It's time consuming and not precise.
2. How to trigonometry, using the arguments of trigonometry to add and subtract two sinusoids. This method is difficult and time consuming.
3. How da complex algebraic phasor analysis as described earlier. Aiani is the easiest way.

power Fasor and power complex
From the preceding discussion can be seen that the average power is not a function of current and voltage rms, but there are distinctive elements of the current and voltage phase angle.

Voltage multiplied by current is called pseudo-power. The average power divided by apparent power is called power factor.

If a given load voltage, the impedance of the load, the impedance of the load will determine the amount of current flowing and the phase angle on the load. Power factor is an indication that states the nature of a burden.

Calculation of 3-phase
Almost all the electricity used by industry, generated, transmitted, and distributed in 3 phase system. These systems have the same magnitude for voltage or current but have different angles of 120˚ between them phase

If the source supplies a balanced load, the current flowing in each of the Conductor will have the same magnitude and phase angle different from 120 ˚ to each other. This current flow is called balanced.

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AC Generation Analysis

Analysis of the AC power generation process and of the alternating current we use in almost every aspect of our lives is necessary to better understand how AC power is used in today’s technology.

Effective Values

The output voltage of an AC generator can be expressed in two ways. One is graphically by use of a sine wave (Figure 1). The second way is algebraically by the equation e = Emax sin wt, which will be covered later in the text.

Figure 1 Voltage Sine Wave

When a voltage is produced by an AC generator, the resulting current varies in step with the voltage. As the generator coil rotates 360°, the output voltage goes through one complete cycle. In one cycle, the voltage increases from zero to Emax in one direction, decreases to zero, increases to Emax in the opposite direction (negative Emax), and then decreases to zero again. The value of Emax occurs at 90° and is referred to as peak voltage. The time it takes for the generator to complete one cycle is called the period, and the number of cycles per second is called the frequency (measured in hertz).

One way to refer to AC voltage or current is by peak voltage (Ep) or peak current (Ip). This is the maximum voltage or current for an AC sine wave.

Another value, the peak-to-peak value (Ep-p or Ip-p), is the magnitude of voltage, or current range, spanned by the sine wave. However, the value most commonly used for AC is effective value. Effective value of AC is the amount of AC that produces the same heating effect as an equal amount of DC. In simpler terms, one ampere effective value of AC will produce the same amount of heat in a conductor, in a given time, as one ampere of DC. The heating effect of a given AC current is proportional to the square of the current. Effective value of AC can be calculated by squaring all the amplitudes of the sine wave over one period, taking the average of these values, and then taking the square root. The effective value, being the root of the mean (average) square of the currents, is known as the root-mean-square, or RMS value. In order to understand the meaning of effective current applied to a sine wave, refer to Figure 2.

The values of I are plotted on the upper curve, and the corresponding values of I^2 are plotted on the lower curve. The I2 curve has twice the frequency of I and varies above and below a new axis. The new axis is the average of the I^2 values, and the square root of that value is the RMS, or effective value, of current. The average value is ½ Imax^2. The RMS value is then, 2^(1/2)Imax^2/ 2 or 2^(1/2)/2 x Imax, which is equal to 0.707 Imax.
There are six basic equations that are used to convert a value of AC voltage or current to another value, as listed below.

1. Average value = peak value x 0.637……………….(1)
2. Effective value (RMS) = peak value x 0.707………(2)
3. Peak value = average value x 1.57…………………(3)
4. Effective value (RMS) = average value x 1.11…….(4)
5. Peak value = effective value (RMS) x 1.414………(5)
6. Average value = effective (RMS) x 0.9……………(6)

The values of current (I) and voltage (E) that are normally encountered are assumed to be RMS values; therefore, no subscript is used.

Figure 2 Effective Value of Current

Another useful value is the average value of the amplitude during the positive half of the cycle.
Equation (7) is the mathematical relationship between Iav , Imax , and I.

Iav = 0.637 Imax = 0.90 I………….(7)

Equation (8) is the mathematical relationship between Eav , Emax , and E.

Eav = 0.637 Emax = 0.90 E……….(8)

Example 1: The peak value of voltage in an AC circuit is 200 V. What is the RMS value of the voltage?
Solution:
E = 0.707 Emax = 0.707 (200 V) = 141.4 V

Example 2: The peak current in an AC circuit is 10 amps. What is the average value of current in the circuit?
Solution:
Iav = 0.637 Imax = 0.637 (10 amps) = 6.37 amps

Phase Angle

Phase angle is the fraction of a cycle, in degrees, that has gone by since a voltage or current has passed through a given value. The given value is normally zero. Referring back to Figure 1, take point 1 as the starting point or zero phase. The phase at Point 2 is 30°, Point 3 is 60°, Point 4 is 90°, and so on, until Point 13 where the phase is 360°, or zero. A term more commonly used is phase difference. The phase difference can be used to describe two different voltages that have the same frequency, which pass through zero values in the same direction at different times. In Figure 3, the angles along the axis indicate the phases of voltages e1 and e2 at any point in time. At 120°, e1 passes through the zero value, which is 60° ahead of e2 (e2 equals zero at 180°). The voltage e1 is said to lead e2 by 60 electrical degrees, or it can be said that e2 lags e1 by 60 electrical degrees.

Figure 3 Phase Relationship

Phase difference is also used to compare two different currents or a current and a voltage. If the phase difference between two currents, two voltages, or a voltage and a current is zero degrees, they are said to be "in-phase." If the phase difference is an amount other than zero, they are said to be "out-of-phase."

Voltage Calculations

Equation (9) is a mathematical representation of the voltage associated with any particular orientation of a coil (inductor).

e = Emax sin teta........(9)

where
e = induced EMF
Emax = maximum induced EMF
 (teta)= angle from reference (degrees or radians)

Example 1: What is the induced EMF in a coil producing a maximum EMF of 120 V when the angle from reference is 45°?
e = Emax sin teta= 120 V (sin 45°)= 84.84 V

The maximum induced voltage can also be called peak voltage Ep. If (t) is the time in which the coil turns through the angle, teta (), then the angular velocity, w () of the coil is equal to teta/t and is expressed in units of radians/sec. Equation (10) is the mathematical representation of the angular velocity.
teta = wt………….(10)

where
,teta= angular velocity (radians/sec)
t = time to turn through the angle from reference (sec)
,w= angle from reference (radians)

Using substitution laws, a relationship between the voltage induced, the maximum induced voltage, and the angular velocity can be expressed. Equation (11) is the mathematical representation of the relationship between the voltage induced, the maximum voltage, and the angular velocity, and is equal to the output of an AC Generator.

e = Emax sin (wt)……………(11)

where
e = induced EMF (volts)
Emax = maximum induced EMF (volts)
, w = angular velocity (radians/sec)
t = time to turn through the angle from reference (sec)

Current Calculations

Maximum induced current is calculated in a similar fashion. Equation (7-12) is a mathematical representation of the relationship between the maximum induced current and the angular velocity.

i = Imax sin (wt)…………(12)

where
i = induced current (amps)
Imax = maximum induced current (amps)
= ang, wular velocity (radians/sec)
t = time to turn through the angle from reference (sec)


Frequency Calculations

The frequency of an alternating voltage or current can be related directly to the angular velocity of a rotating coil. The units of angular velocity are radians per second, and 2radians is a full revolution. A radian is an angle that subtends an arc equal to the radius of a circle. One radian equals 57.3 degrees. One cycle of the sine wave is generated when the coil rotates 2phi (2 x 3.14) radians. Equation (13) is the mathematical relationship between frequency (f) and the angular velocity, w () in an AC circuit.

w = 2phi.f --> 2 x 3.14 x f………….(13)
where
, w= angular velocity (radians/sec)
f = frequency (HZ)

Example 1: The frequency of a 120 V AC circuit is 60 Hz. Find the following:
1. Angular velocity
2. Angle from reference at 1 msec
3. Induced EMF at that point

Solution:
1. w= 2phi.f = 2 (3.14) (60 Hz) = 376.8 radians/sec
2. teta = wt = (376.8 radian/sec) (.001 sec) = 0.3768 radians
3. e = Emax sin teta= (120 V) (sin 0.3768 radians)= (120 V) (0.3679)= 44.15 V

Summary

Voltage, Current, and Frequency Summary

• The following terms relate to the AC cycle: radians/second, the velocity the loop turns; hertz, the number of cycles in one second; period, the time to complete one cycle.
• Effective value of AC equals effective value of DC.
• Root mean square (RMS) values equate AC to DC equivalents:
• I = 0.707 Imax = Effective Current 
• E = 0.707 Emax = Effective Voltage 
• Iav = 0.636 Imax = 0.9 I = Average Current 
• Eav = 0.636 Emax = 0.9 E = Average Voltage
• Phase angle is used to compare two wave forms. It references the start, or zero point, of each wave. It compares differences by degrees of rotation. Wave forms with the same start point are "in-phase" while wave forms "out-of-phase" either lead or lag.

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