The post Maxwell Inductance Bridge Circuit appeared first on Electrical Academia.

]]>Fig.1: Maxwell Bridge

A disadvantage of this bridge is that the standard inductors are larger and difficult to manufacture than standard capacitors. Consequently, a variation of this circuit, known as the Maxwell-Wein Bridge, is most often employed for inductance measurement.

The circuit of the Maxwell-Wein Bridge is shown in figure 2.

Fig.2: Maxwell-Wein Bridge

L_{x} is the unknown inductance to be measured, and r_{x} is the resistance of its windings. C_{s} is again a precise standard capacitor, and P is a standard resistor. Q and S are accurately adjustable resistors.

At balance, we have the following equation:

\[\frac{{{Z}_{1}}}{{{Z}_{2}}}=\frac{{{Z}_{3}}}{{{Z}_{4}}}\]

Therefore,

\[\begin{matrix} \frac{S}{{}^{1}/{}_{(\frac{1}{Q}+j\omega {{C}_{s}})}}=\frac{{{r}_{x}}+j\omega {{L}_{x}}}{P} & \cdots & (1) \\\end{matrix}\]

Or

\[S(\frac{1}{Q}+j\omega {{C}_{s}})=\frac{{{r}_{x}}+j\omega {{L}_{x}}}{P}\]

\[\begin{matrix} \frac{S}{Q}+j\omega {{C}_{s}}S=\frac{{{r}_{x}}}{P}+\frac{j\omega {{L}_{x}}}{P} & \cdots & (2) \\\end{matrix}\]

Equating the real and imaginary terms:

\[\begin{matrix} \frac{S}{Q}=\frac{{{r}_{x}}}{P} & \cdots & (3) \\\end{matrix}\]

And

\[\omega {{C}_{s}}S=\frac{\omega {{L}_{x}}}{P}\]

Once again it is seen that the supply voltage and the frequency are not involved in the balance equations for the bridge. This is not always the case with AC bridges; indeed, one particular bridge can be used to measure the frequency of the supply in terms of the bridge components values at balance.

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]]>The post Series Resistance Capacitance Bridge Circuit appeared first on Electrical Academia.

]]>The circuit of the **series resistance-capacitance bridge** shown in figure 1 eliminates the balance problems that can occur with the simple capacitance bridge. Resistance r_{x} in series with the unknown capacitance represents the resistive component of the capacitor equivalent circuit. The standard capacitor C_{s }normally has mica dielectric and thus has a very small resistive component. Consequently, the adjustable resistance S must be included in the circuit to balance the effect of r_{x}.

The balance equations for the series resistance capacitance bridge are derived as follows:

\[\frac{{{Z}_{1}}}{{{Z}_{2}}}=\frac{{{Z}_{3}}}{{{Z}_{4}}}\]

Therefore,

\[\frac{S-j\frac{1}{\omega {{C}_{s}}}}{Q}=\frac{{{r}_{x}}-j\frac{1}{\omega {{C}_{x}}}}{P}\]

\[\begin{matrix} \frac{S}{Q}-j\frac{1}{\omega {{C}_{s}}Q}=\frac{{{r}_{x}}}{P}-j\frac{1}{\omega {{C}_{x}}P} & \cdots & (1) \\\end{matrix}\]

For equation (1) to be correct, the real parts on each side must be equal, and the imaginary parts on each side must be equal.

Equating the real parts,

\[\frac{S}{Q}=\frac{{{r}_{x}}}{P}\]

And

Fig.1: Series Resistance Capacitance Bridge

The use of series resistors with a capacitance bridge makes balance easy to obtain and allows the resistive component of the capacitors to be measured.

Now, equating the imaginary parts,

\[\frac{1}{\omega {{C}_{s}}Q}=\frac{1}{\omega {{C}_{x}}P}\]

And

The resistive and capacitive components of the unknown capacitance can now be calculated by means of equations (2) and (3). Note that neither the supply voltage nor the AC frequency is involved in the balance equations for the bridge.

Because of the need to balance the real and imaginary components of the bridge impedances, the process of obtaining balance in an AC bridge is a little more complicated than with the Wheatstone bridge. One of the adjustable components (Q or S in figure 1) is first altered to obtain the lowest possible indication of the null meter. Then the other adjustable component is varied to obtain the lowest reading. The process is repeated until further adjustment of either component cannot produce lower reading on the null meter. At this point the bridge is balanced.

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]]>The post Capacitance Bridge Working Principle appeared first on Electrical Academia.

]]>Figure 1(a) shows the circuit of a simple capacitance bridge. C_{s} is a precise standard capacitor, C_{x} is an unknown capacitance, and Q and P are standard resistors, one or both of which is adjustable. An AC supply is used, and the null detector (D) must be an AC instrument. A low-current rectifier ammeter is frequently employed as a null detector. Q is adjusted until the null detector indicates zero, and when this is obtained, the bridge is said to be balanced.

Fig.1: (a) Simple Capacitance Bridge

When the detector indicates null, the voltage drop across C_{s} must equal that across C_{x}, and similarly, the voltage across Q must be equal to the voltage across P. therefore,

$\begin{align} & {{V}_{cs}}={{V}_{cx}} \\ & or \\ & \begin{matrix} {{i}_{1}}{{X}_{cs}}={{i}_{2}}{{X}_{cs}} & \cdots & (1) \\\end{matrix} \\\end{align}$

And

\[\begin{align} & {{V}_{Q}}={{V}_{P}} \\ & or \\ & \begin{matrix} {{i}_{1}}Q={{i}_{2}}P & \cdots & (2) \\\end{matrix} \\\end{align}\]

Dividing equation (1) by equation (2):

\[\begin{matrix} \frac{{{X}_{cs}}}{Q}=\frac{X{}_{cx}}{P} & \cdots & (3) \\\end{matrix}\]

Referring to equation (3) and figure 1(b), the general balance equation for all AC bridges can be written as:

Fig.1(b): General circuit diagram for an AC bridge

$\begin{matrix} \frac{{{Z}_{1}}}{{{Z}_{2}}}=\frac{{{Z}_{3}}}{{{Z}_{4}}} & \cdots & (4) \\\end{matrix}$

Substituting 1/ωC_{s }for X_{cs} , and 1/ωC_{x }for X_{cx} in equation (3),

$\begin{align} & \frac{1}{\omega {{C}_{s}}Q}=\frac{1}{\omega {{C}_{x}}P} \\ & or \\ & {{C}_{x}}=\frac{Q\omega {{C}_{s}}}{P\omega } \\\end{align}$

Giving

It is seen that the unknown capacitance C_{x} can now be calculated from the known values of Q, C_{s}, and P.

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]]>The post Phase Rotation Meter | Phase Sequence Indicator appeared first on Electrical Academia.

]]>

Fig.1: Phase Rotation Tester

An operation where the motor is supposed to spin in the clockwise rotation the phase order is normally AØ, BØ, and CØ, and operation, where the motor supposed to spin in a counterclockwise rotation, means that the phase order is usually CØ, BØ, and AØ. Due to limited access to the wiring from the electrical system is important to use the phase rotation meter to determine the phase order.

In this type of meter, a couple of arrangements of lamps with capacitor or inductor are employed in order to point out the phase sequence. The proportionate brightness level and darkness of lamps determine the sequence of given three-phases. The following two arrangements are utilized for determining the phase sequence of given three phase supply.

In the first arrangement, an inductor and two lamps are linked in a way that two phases (A and B) comprise of lamps as loads and third phase (C) holds an inductor as shown in the figure.

Fig.2: Inductor type Static Phase Sequence Meter

When the meter is connected to the three phase supply, the first lamp shines dimmer whereas the second lamp beams brighter for ABC phase sequence. For phase sequence ACB, the first lamp shines brighter whilst second lamp radiates dimmer.

In the second arrangement, standard lamps are substituted with neon ones and a capacitor is used rather than an inductor. It is to be mentioned that neon lamp does not glow at a voltage less than its breakdown voltage and this property avoids the uncertainness of bright and dim statuses of lamps of former inductor type indicator.

Fig.3: Capacitor type Static Phase Sequence Meter

The phase sequence is considered ABC if the first lamp shines bright whilst second lamp does not shine at all. If the first lamp stays dark whereas the second lamp shines bright, then the phase sequence is ACB.

- Locate and turn off main breaker supply.
- Connect the phase rotation meter alligator clips to the exposed copper or metal of the leads to be tested.
- Turn main breaker supply on.
- Observe the meter for rotation.
- Turn main breaker supply off and remove alligator clips from the circuit.

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]]>The post Digital Multimeter Working Principle appeared first on Electrical Academia.

]]>Fig.1: Digital Multimeter

There are two main types of multimeters. One of the first and oldest multimeters is the analog meter, (Figure 2) and the other, now more widely used meter is the digital multimeter (Figure 1).

Fig.2: Analog Multimeter

Analog meters are a multifunctional multimeter that operates based on electrical mechanical movement. Analog meters use a printed linear or nonlinear background and a mechanical pointer. The pointer moves as a result of the flow of current through a built-in coil, the presence of electrical pressure, or the internal power source that is needed for resistance measurements. The advantage of an analog meter is relatively small; however, it allows you to see small changes in current flow and a change in voltage in real time. Analog meters require great mathematical skills because you are required to make quick calculations based on the printed scale. Time used while calculating mathematical solutions while taking a reading with an analog meter could be better used to resolve other problems.

A digital multimeter (DMM) is a multifunctional meter that displays its electrical quantitative values on an LCD screen. A digital multimeter much like an analog meter, it is able to read voltage, current, and resistance. What makes a digital multimeter differ from the analog meter is its ability to display measured electrical values quickly without any computations. Because of its design, a processor can be built into the meter which allows the user to take measurements of frequency, the inductance of a coil, capacitance of a capacitor, and a host of other high functional electrical measurements. There two types of digital multimeters (DMM): **scalable digital multimeter** and **auto-ranging digital multimeter** as shown in Figure 1. When working with the scalable digital multimeter you need to have an idea of the value of voltage, current, or resistance that you are attempting to measure. Failure to observe these values will result in inaccurate readings and possible damage to the meter. The auto-ranging digital multimeter is more widely used due to its ease, high functionality, and quick display readings achieved without the user completing the calculations.

The auto-ranging digital multimeter (DMM) only requires you to choose your electrical quantity you are attempting to measure, make sure you are properly placing your leads into the correct terminals and then reading the LCD display. Auto-ranging digital multimeters allow technicians to spend more time getting to the root of a problem instead of switching and calculating.

Testing for voltage is carried out to ensure the effectiveness of the electrical system. Loads (for example lights or motors) that are designed to do the work need a nominal voltage to operate. Over voltage will result in equipment failure and not enough voltage will result in the load not turn on. When testing voltage there is an expected voltage reading to look for. If the load is rated at 120 volts then the expected reading from the outlet needs to be 120 volts plus or minus 10%. If the voltage reading is out of specifications then the problem can be found using the volt meter to isolate the load and find if there is a problem with the source or the load.

Here is a step by step guide on how to use a multimeter to test for voltage:

- First, figure out whether the application being testing utilizes AC or DC voltage. Afterward, adjust the meter dial to the suitable function to DC Voltage or AC voltage.
- Adjust the range to the number little higher than the predictive value. If the value being measured is unknown, then set the range to the maximum available number.
- Plug in the test leads into the common (black) and voltage (red) terminals.
- Apply the leads to the test circuit.
- Position and reposition the test till a dependable reading appears on the meter LCD.
- While measuring AC voltage, variations may happen in the reading. As the test continues the measurement will steady.

Testing for current is used when there is no physical way to tell if a load is doing its job because there are no indicators or the load is located in a hazardous area. When the voltage is tested and found to be present at the load, it doesn’t tell the whole story until a current is measured. It is important to understand a load consumes power which is measured in watts. Watts is calculated by multiplying volts by the amps. A digital multimeter is used to measure or give a good indication of current flowing.

Current can be tested in several ways; the most reliable procedure is using a clamp meter, shown in figure 3.

Fig.3: Clamp Meter

The advantage of using clamp meter is that measurements can be obtained even without opening the test circuit. Proper protective equipment must be worn before testing can be done.

- To test for current, determine the type of current if it is AC or DC.
- Afterward, adjust the meter dial to the suitable function to DC current or AC current.
- Adjust the range on the dial except it is an auto-ranging meter.

- Press the thumb lever to open the clamp meter head
- Close the head once it is around a single conductor and then release the metering lever.
- Now observe the reading.

- Plug the leads into the terminals marked mA for low current or A for currents over 500mA.
- Set the dial to AC or DC current depending on the circuit being measured.
- Apply the leads to the open circuit current and observe the measurement.

**Note: ** For current measurements above 1A, normally clamp meter is used while for current less than 1A, a standard DMM is used.

Resistance testing is done to ensure the load or circuit being tested is complete. A complete circuit means there is no break or opening in the wires connected to the load or the internal components of the device being tested. An open circuit or broken line means that the load will not work as designed. Resistance testing is sometimes referred to as continuity testing. Continuity testing does the same action as resistance testing with the exception that continuity testing emits an audible sound indicating that the circuit or wires are complete. The resistance testing and continuity testing are also a good way to check for short-circuits and the ground fault which are events that cause circuit breakers to trip, fuses to blow, and possible injury to workers in the field.

- Turn the power off in the circuit being tested.
- Adjust the meter dial to the resistance mode.
- Choose the suitable range on the dial.
- Plug in your test leads into the suitable terminals.
- Connect the leads to the component being tested and note a reading.

**Note**: It is important to have good contact between the test leads and circuit being tested. Dirt, bodily contact, and poor test lead connection can considerably alter the readings.

- Adjust the dial to the meter continuity (the little speaker) function.
- Plug the test leads into the suitable terminal.
- Touch the component under test using the leads

The DMM beeps under good continuity that allows the flow of current. If no continuity exists, the DMM does not beep.

written by *Ahmed Faizan, M.Sc. (USA)*

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]]>The post Dynamometer Type Wattmeter Working Principle | Electrodynamometer appeared first on Electrical Academia.

]]>P=EI

However, it is much more convenient to have an instrument that indicates power directly. The meter used for this purpose is called a wattmeter, and the instrument that can be applied as a wattmeter is known as a dynamometer, or sometimes as an electrodynamic instrument. The construction of a dynamometer instrument to some extent resembles the PMMC instrument. The major difference from the PMMC construction is that the permanent magnet is replaced by two coils, as illustrated in figure (1). The magnetic field in which the lightweight moving coil is situated is generated by passing current through the fixed field coils. Then, when a current is passed through the moving coil, the moving coil and the meter pointer are deflected.

Fig.1: Dynamometer Instrument

The deflection of the pointer of a dynamometer instrument is proportional to the current through the moving coil, but it is also proportional to the flux density of the magnetic field set up by the fixed field coils. This means, of course, the deflection is also proportional the current through the fixed field coils.

Consider the arrangement shown in figure 1. The moving coil of the instrument has a series resistor and is connected in parallel with the load. Consequently, current I_{v} through the moving coil is directly proportional to the load voltage. The field coils are connected in series with the load, so the current flowing through them is (I_{v}+I_{L}), as shown. If I_{v}<<I_{L}, I_{v} can be neglected and the field coil current assumed to be approximately equal to I_{L}. Because the meter deflection is proportional to the field coil current and to the moving coil current,

$deflection\text{ }\alpha \text{ }V{}_{L}*{{I}_{L}}$

or

$deflection\text{ }\alpha \text{ }P$

The scale of the instrument can be calibrated to indicate watts, and thus it becomes a dynamometer type wattmeter.

The scale of the wattmeter is illustrated in figure 2 in which upper scale is calibrated in milli-watts while the lower one measures the power in watts range.

Fig.2: Wattmeter Scale

Because fairly large currents are required to set up the necessary field flux, the dynamometer instrument is not as sensitive as a PMMC instrument. Consequently, its major application is as a wattmeter. One advantage that the dynamometer has over a PMMC instrument is that it can be used for both direct and alternating current/voltage instruments.

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]]>The post Megohmmeter Working Principle | Megger Working Principle appeared first on Electrical Academia.

]]>A high voltage source is required to pass a measurable current through such resistances. Thus, the megger is essentially an ohmmeter with a sensitive deflection instrument and a high voltage source. As illustrated in figure (1), the voltage is usually produced by a hand-cranked generator. The generated voltage may range from 100 V to 2.5 kV.

Fig.1: Hand-Cranked Megohmmeter

As in the case of a low resistance ohmmeter, the scale of the megger indicates infinity (∞) when measuring an open-circuit, zero on a short-circuit, and half-scale when the unknown resistance equals a standard resistor inside the megohmmeter. At other points on the scale, the deflection is proportional to the ratio of the unknown and standard resistors. The range of the instrument can be altered by switching different values of the standard resistor into the circuit.

**Battery powered Megohmmeters** are also available, and these are essentially very high resistance ohmmeters. The battery voltage is typically increased (by electronic circuitry) to a level of 1000V in order to produce a measurable current through the unknown resistance. The measurement is made when the power button is pressed and hold briefly. This action minimizes the drain current on the battery.

A **Megohmmeter** is also used to detect insulation failure within motors and transformers. This is achieved by inducing high voltages into the windings of these electrical components. The introduction of a large amount of voltage will result in the detection of weakened insulation; most likely will lead to motor failure or transformer short-circuiting. **The voltages used in Megger insulation testing can range from 50 V to 5000 V.** By inducing a high voltage into the windings of a motor or transformer, you will be able to detect if there is insulation deterioration. If so, current will flow out of the windings. Escaping current can possibly result in a ground fault or a short-circuiting of the motor or transformer windings.

Figure 3 shows the detailed circuit diagram of Megohmmeter.

Fig.3: Megohmmeter Circuit Diagram

**1 and 2: Control and Deflecting Coil**

They are typically mounted to each other at an angle of 90 degrees and linked to the generator in a parallel manner. The polarities are in such a way that the torque developed by these coils is in opposite direction.

**3 and 4: Scale and Pointer**

A pointer is tied to the coils and end of the pointer moves on a meter scale having a range between “zero” and “infinity”. The scale is calibrated in “ohms”.

**5 and 6: Pressure Coil and Current Coil resistances**

They provide protection against any damage in case of low external resistance under test.

**7: D.C generator or battery connection**

In manually operated megger, a DC generator provides test voltage while in digital type megger, this is done by battery or voltage charger.

**8: Permanent Magnets**

Permanent magnets generate a magnetizing effect in order to deflect the pointer.

- Isolate the equipment to be tested from all power circuits
- Connect leads to the appropriate terminals for insulation testing
- Set the function switch to the desired voltage the meter will induce into the electrical component

** Note:** It is important to check with the manufacturer about performing insulation testing and ratings of the electrical component before proceeding. Too much voltage can void the warranty, shorten the life, or cause damage to the motor or transformer being tested.

- Connect tips of the test leads to the equipment to be tested. If there is a voltage present most meters will give some type of warning.
- Follow the equipment manual and begin the test.

When testing between the windings and earth ground the result should be zero resistance. If there is some type of resistance between the windings and earth ground, the result will be a ground fault at this point and it is important to replace the unit.

When testing between two separate windings the result should be close to zero. If there is some type of resistance between the two separate windings this is an indication that the insulation is breaking down at this point and is important to plan for the equipment to be replaced.

written by *Ahmed Faizan, M.Sc. (USA)*

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]]>The post PMMC Instrument Working Principle | Permanent Magnet Moving Coil Instrument appeared first on Electrical Academia.

]]>Figure 1 shows the basic construction of a PMMC instrument. A moving-coil instrument contains principally of a permanent magnet to offer a magnetic field and a small lightweight coil pivoted within the field. A soft iron core is included between the poles of the magnet so that the coil rotates in the narrow air gap between the poles and the core. When a current is passed through the coil windings, a torque is exerted on the coil by the interaction of the magnet’s field and the field set up by the current in the coil. The resulting deflection of the coil is indicated by a pointer that moves over a calibrated scale.

Fig.1: PMMC Basic Construction

In addition to a deflecting force provided by the coil current and the field from the permanent magnet, a controlling force is needed. This is the force that returns the coil and pointer to the zero position when no current is flowing through the coil. The controlling force also balances the deflecting force, so that the pointer remains stationary for any constant level of current through the coil. The controlling force is usually provided by spiral springs as indicated in figure 2. The springs are also employed as connecting leads for conducting current through the coil.

Fig.2: PMMC Coil Springs

One other force, known as a damping force, is required for correct operation of a deflection instrument. When no damping force is present, the pointer swings above and below its final position on the scale for some time before settling down. In the case of the PMMC instruments, the damping force uses eddy currents. To facilitate this, the coil is wound on an aluminum frame or coil former in which eddy currents are generated by any rapid movements of the coil in the magnetic field. The eddy currents set up a magnetic flux that opposes the original movement that generates them. Thus, oscillations of the meter pointer are damped out.

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]]>The post Wire Gauge Sizes | Circular mils appeared first on Electrical Academia.

]]>The standardized unit for wire cross-sectional area is circular mil. Since the round conductor’s diameter is generally a small fraction of an inch, it is quite handy to demonstrate them in mils, which is equivalent to 1/1000 of an inch, for avoiding the use of decimals.

For instance, the conductor diameter can be stated as 25 mils instead of 0.025 in. A circular mil, in fact, is the area of a circle whose diameter is one mil, as depicted in figure 1.

Fig.1: Circular Mil

The area of a round conductor in circular mils is acquired by squaring up the diameter which is calculated in mils. This convention is an engineering agreement which is in practice for last many decades and is not quite associated to the circle area being equivalent to $\pi {{r}^{2}}$.

Example

What is the circular mil area of a round conductor with a diameter of 25 mils?

Solution

$A={{d}^{2}}={{25}^{2}}=635\text{ c}\text{.mils}$

A circular mil-foot, as demonstrated in figure 2, is, in reality, a volume unit. It holds a one circular mil cross-sectional area and a length of one foot. Since it is conceived a unit conductor, the circular mil-foot is very valuable in order to make comparisons between conductors formed of dissimilar metallic elements. For instance, a resistivity comparison of different conductors’ types can be made by finding out the resistance of a circular mil-foot of each conductor.

Fig.2: Circular Mil-Foot

The resistance of a conductor expressed in ohms per unit length per unit area, that is, per circular mil-foot.

Specific Resistance can be described as the resistance (calculated in ohms) offered by a unit volume (which is equivalent to the circular mil-foot) of a substance (material) to the electrical current flow. A substance that possesses higher resistivity will offer low conductivity, and vice versa. For instance, the cooper specific resistance is $10.4\text{ }{}^{\Omega }/{}_{mil-ft}$ . Put differently, a copper conductor of the cross-sectional area and a length of 1 foot possesses 10.4 Ω resistance.

A list of specific resistivities of several different types of materials is given in table 1. The values indicated are based on 20 ^{o}C.

Material Resistivity
Silver 9.56
Copper 10.4
Gold 14
Aluminum 17
Tungsten 34
Brass 42
Iron 61
Nichrome 675

Table 1: Specific Resistivities (${}^{\Omega }/{}_{c.mil-ft}$ at 20 ^{o}C)

The relationship of specific resistance, length, and cross-sectional area is given by the following equation:

$R=\rho \frac{L}{A}$

Where

ρ= specific resistance

L= length in feet

A= cross-section area in circular mils

The following example illustrates the use of this formula.

**Example**

Calculate the resistance of a piece of copper wire at 20 ^{o}C if it is 25 ft long and 40 mils in diameter.

**Solution**

$A={{d}^{2}}={{25}^{2}}=1600\text{ c}\text{.mils}$

Substitute in the above mentioned formula, we come up with

$R=10.4*\frac{25}{1600}=0.163\text{ }\Omega $

The system of notation for measuring the size of conductors or wires.

Wires are manufactured in sizes numbered according to the American wire gage (AWG). Some of these numbers appear in Table 1. Notice that the wire diameters become smaller as the gage numbers increase. In typical applications, where the current is mill amperes, a #22 number wire would be used. By comparison, a #14 wire is customarily used in residential-lightning circuits and #12 for wall plugs. When any conductor is selected, consideration must be given to the maximum current it can safely carry and the voltage its insulation can stand without breakdown.

Gage number Diameter (mils) Circular mil area Ohms per 1000 ft
0 365 133000 0.0795
0 325 106000 0.1
1 289 83700 0.126
2 258 66400 0.159
3 229 52600 0.201
4 204 41700 0.253
5 182 33100 0.319
6 162 26300 0.403
7 144 20800 0.508
8 128 16500 0.641
9 114 13100 0.808
10 102 10400 1.02
11 91 8230 1.28
12 81 6530 1.62
13 72 5180 2.04
14 64 4110 2.58
15 57 3260 3.25
16 51 2580 4.09
17 45 2050 5.16
18 40 1620 6.51
19 36 1290 8.21
20 32 1020 10.4
21 28.5 810 13.1
22 25.3 642 16.5
23 22.6 509 20.8
24 20.1 404 26.2
25 17.9 320 33
26 15.9 254 41.6
27 14.2 202 52.5
28 12.6 160 66.2
29 11.3 127 83.4
30 10 101 105
31 8.9 79.7 133
32 8 63.2 167
33 7.1 50.1 211
34 6.3 39.8 266
35 5.6 31.5 335
36 5 25 423

Table.2: American Wire Gauge (AWG) Wire Sizes

Copper is most frequently used for wire conductors because it has a low resistance per unit length, is less expensive than silver or gold, and is easily solderable. The copper is usually tinned (covered with a thin coating of solder) and may be solid or stranded.

Twin-lead transmission line

A type of transmission line comprised of two parallel conductors covered by a solid insulation.

Coaxial cable

A transmission line in which one conductor is concentric to another and separated by a continuous solid dielectric spacer.

Many electric cables are used in industry to interconnect components. Cables consist of two or more conductors within a common covering. Figure 1 shows a typical 300 Ω twin-lead transmission line, or cable, such as used in TV to connect the antenna to the receiver.

Fig.3: Twin-Lead Transmission Line

The cable shown in figure 2 is a coaxial cable, which is used extensively for conducting high-frequency currents and consists of an inner conductor surrounded by polyethylene or other highly resistive insulation. Over the insulation is a flexible, tinned copper braid, which is in turn enclosed in a vinyl jacket. The inner conductor and braid constitute the two leads.

Fig.4: Coaxial Cable

Although aluminum has only about 60 % of the conductivity of copper, it is much lighter in weight than copper and is now frequently used by the electrical power companies. Because aluminum conductors are not easily soldered, lugs, or terminals, are generally fastened to them by special tools.

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]]>The post Impedance Measurement Theory appeared first on Electrical Academia.

]]>$Z={}^{V}/{}_{I}$

We can obtain the magnitude of circuit impedance. However, it is often desirable to separate impedance into resistive and reactive components. One instrument that is used to measure the separate resistive and reactive parts of an impedance is the AC Bridge. The circuit of the general AC Bridge is shown in figure 1.

Fig.1: The AC Bridge Circuit

The configuration is similar to that of the Wheatstone bridge, yet distinct differences exist between the components. The AC Bridge has impedance arms, rather than resistance arms; instead of a battery and galvanometer, an AC signal source and null detector are used. If the signal voltage is in the audio range, a set of headphones may be used as the null detector; otherwise, a sensitive AC Voltmeter is used.

As in the Wheatstone bridge, at balance, no current flows through the detector. The voltage from a to c equals that from a to d, so that

${{I}_{1}}{{Z}_{1}}={{I}_{3}}{{Z}_{3}}\text{ (1)}$

Similarly,

${{I}_{2}}{{Z}_{2}}={{I}_{x}}{{Z}_{x}}\text{ (2)}$

It follows that for balanced conditions

\[\frac{{{Z}_{1}}}{{{Z}_{2}}}=\frac{{{Z}_{3}}}{{{Z}_{x}}}\]

\[{{Z}_{x}}={{Z}_{3}}\left( \frac{{{Z}_{2}}}{{{Z}_{1}}} \right)\text{ (3)}\]

In order to obtain balance, at least one of the unknown impedances must have a resistive and reactive components. If Z_{3} is chosen to be complex, Z_{1} and Z_{2} can be conveniently chosen to be purely resistive with a ratio that is a power of 10. Then from equation (3),

${{R}_{x}}+j{{X}_{x}}=({{R}_{3}}+j{{X}_{3}})\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)\text{ (4)}$

For equation (4) to be satisfied, the real parts of both sides must be equal, and also the imaginary parts of both sides. Equating these parts, we obtain

\[{{R}_{x}}={{R}_{3}}\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)\text{ (5)}\]

\[{{X}_{x}}={{X}_{3}}\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)\text{ (6)}\]

A simple inductance bridge is shown in figure 2.

Fig.2: An Inductance Bridge

When the bridge is balanced, we solve for R_{x} by using equation (5). From equation (6), we then solve for the inductance L_{x},

\[\omega {{L}_{x}}=\omega {{L}_{3}}\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)\text{ }\]

Or

\[{{L}_{x}}={{L}_{3}}\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)\text{ (7)}\]

Here, from equation (7), we can easily obtain the unknown inductance in the circuit.

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