Tuesday 3 June 2014

DC circuit equations and laws

DC circuit equations and laws



Ohm's and Joule's Laws



NOTE: the symbol "V" ("U" in Europe) is sometimes used to represent voltage instead of "E". In some cases, an author or circuit designer may choose to exclusively use "V" for voltage, never using the symbol "E." Other times the two symbols are used interchangeably, or "E" is used to represent voltage from a power source while "V" is used to represent voltage across a load (voltage "drop").


Kirchhoff's Laws

"The algebraic sum of all voltages in a loop must equal zero."

Kirchhoff's Voltage Law (KVL)



"The algebraic sum of all currents entering and exiting a node must equal zero."

Kirchhoff's Current Law (KCL)
DC circuit equations and laws



Ohm's and Joule's Laws



NOTE: the symbol "V" ("U" in Europe) is sometimes used to represent voltage instead of "E". In some cases, an author or circuit designer may choose to exclusively use "V" for voltage, never using the symbol "E." Other times the two symbols are used interchangeably, or "E" is used to represent voltage from a power source while "V" is used to represent voltage across a load (voltage "drop").


Kirchhoff's Laws

"The algebraic sum of all voltages in a loop must equal zero."

Kirchhoff's Voltage Law (KVL)



"The algebraic sum of all currents entering and exiting a node must equal zero."

Kirchhoff's Current Law (KCL)




Ohm's and Joule's Laws



NOTE: the symbol "V" ("U" in Europe) is sometimes used to represent voltage instead of "E". In some cases, an author or circuit designer may choose to exclusively use "V" for voltage, never using the symbol "E." Other times the two symbols are used interchangeably, or "E" is used to represent voltage from a power source while "V" is used to represent voltage across a load (voltage "drop").


Kirchhoff's Laws

"The algebraic sum of all voltages in a loop must equal zero."

Kirchhoff's Voltage Law (KVL)



"The algebraic sum of all currents entering and exiting a node must equal zero."

Kirchhoff's Current Law (KCL)

Sunday 1 June 2014

AMMETR

AMMETER



"Amperemeter" redirects here. For the unit of measurement, see Ampere-meter.
Demonstration model of a moving iron ammeter. As the current through the coil increases, the plunger is drawn further into the coil and the pointer deflects to the right.
Wire carrying current to be measured.
Spring providing restoring force
This illustration is conceptual; in a practical meter, the iron core is stationary, and front and rear spiral springs carry current to the coil, which is supported on a rectangular bobbin. Furthermore, the poles of the permanent magnet are arcs of a circle.
Ammeter from the old Penn StationTerminal Service Plant in New York City
Zero-center ammeter
An older moving iron ammeter with its characteristic non-linear scale and with the moving iron ammeter symbol mounted on asmall form factor PC.
An ammeter is a measuring instrument used to measure the electric current in acircuit. Electric currents are measured in amperes (A), hence the name. Instruments used to measure smaller currents, in the milliampere or microampere range, are designated as milliammeters or microammeters. Early ammeters were laboratory instruments which relied on the Earth's magnetic field for operation. By the late 19th century, improved instruments were designed which could be mounted in any position and allowed accurate measurements in electric power systems.
History[edit]
The relation between electric current, magnetic fields and physical forces was first noted by Hans Christian Ørsted who, in 1820, observed a compass[1]
 needle was deflected from pointing North when a current flowed in an adjacent wire. The tangent galvanometer was used to measure currents using this effect, where the restoring force returning the pointer to the zero position was provided by the Earth's magnetic field. This made these instruments usable only when aligned with the Earth's field. Sensitivity of the instrument was increased by using additional turns of wire to multiply the effect – the instruments were called "multipliers".

Types[edit]

Moving-coil[edit]

The D'Arsonval galvanometer is a moving coil ammeter. It uses magneticdeflection, where current passing through a coil causes the coil to move in amagnetic field. The modern form of this instrument was developed by Edward Weston, and uses two spiral springs to provide the restoring force. The uniform air gap between the iron core and the permanent magnet poles make the deflection of the meter linearly proportional to current. These meters have linear scales. Basic meter movements can have full-scale deflection for currents from about 25microamperes to 10 milliamperes.[2]
Because the magnetic field is polarised, the meter needle acts in opposite directions for each direction of current. A DC ammeter is thus sensitive to which way round it is connected; most are marked with a positive terminal, but some have centre-zero mechanisms[note 1] and can display currents in either direction. A moving coil meter indicates the average (mean) of a varying current through it,[note 2] which is zero for AC. For this reason moving-coil meters are only usable directly for DC, not AC.
This type of meter movement is extremely common for both ammeters and other meters derived from them, such as voltmeters and ohmmeters. Although their use has become less common in recent decades, this type of basic movement was once the standard indicator mechanism for any analogue displays involving electrical machinery.

d permanent magnet to provide the restoring force.

Electrodynamic[edit]

An electrodynamic movement uses an electromagnet instead of the permanent magnet of the d'Arsonval movement. T

Moving magnet[edit]

Moving magnet ammeters operate on essentially the same principle as moving coil, except that the coil is mounted in the meter case, and a permanent magnet moves the needle. Moving magnet Ammeters are able to carry larger currents than moving coil instruments, often several tens of Amperes, because the coil can be made of thicker wire and the current does not have to be carried by the hairsprings. Indeed, some Ammeters of this type do not have hairsprings at all, instead using a fixehis instrument can respond to both alternating and direct current[2] and also indicates true RMS for AC. See Wattmeter for an alternative use for this instrument.

Moving-iron[edit]

Moving iron ammeters use a piece of iron which moves when acted upon by the electromagnetic force of a fixed coil of wire. This type of meter responds to both directand alternating currents (as opposed to the moving-coil ammeter, which works on direct current only). The iron element consists of a moving vane attached to a pointer, and a fixed vane, surrounded by a coil. As alternating or direct current flows through the coil and induces a magnetic field in both vanes, the vanes repel each other and the moving vane deflects against the restoring force provided by fine helical springs.[2] The deflection of a moving iron meter is proportional to the square of the current. Consequently such meters would normally have a non linear scale, but the iron parts are usually modified in shape to make the scale fairly linear over most of its range. Moving iron instruments indicate the RMS value of any AC waveform applied.
The moving-iron meter was invented by Austrian engineer Friedrich Drexler in 1884.[3]

Hot-wire[edit]

In a hot-wire ammeter, a current passes through a wire which expands as it heats. Although these instruments have slow response time and low accuracy, they were sometimes used in measuring radio-frequency current.[2] These also measure true RMS for an applied AC current.

Digital[edit]

In much the same way as the analogue ammeter formed the basis for a wide variety of derived meters, including voltmeters, the basic mechanism for a digital meter is a digital voltmeter mechanism, and other types of meter are built around this.
Digital ammeter designs use a shunt resistor to produce a calibrated voltage proportional to the current flowing. This voltage is then measured by a digital voltmeter, through use of an analog to digital converter (ADC); the digital display is calibrated to display the current through the shunt. Such instruments are generally calibrated to indicate the RMS value for a sine wave only but some designs will indicate true RMS (sometimes with limitations as to wave shape).


VOLTMETER

VOLTMETER

voltmeter is an instrument used for measuring electrical potential difference between two points in an electric circuit. Analog voltmeters move a pointer across a scale in proportion to the voltage of the circuit; digital voltmeters give a numerical display of voltage by use of an analog to digital converter.
Voltmeters are made in a wide range of styles. Instruments permanently mounted in a panel are used to monitor generators or other fixed apparatus. Portable instruments, usually equipped to also measure current and resistance in the form of a multimeter, are standard test instruments used in electrical and electronics work. Any measurement that can be converted to a voltage can be displayed on a meter that is suitably calibrated; for example, pressure, temperature, flow or level in a chemical process plant.
General purpose analog voltmeters may have an accuracy of a few percent of full scale, and are used with voltages from a fraction of a volt to several thousand volts. Digital meters can be made with high accuracy, typically better than 1%. Specially calibrated test instruments have higher accuracies, with laboratory instruments capable of measuring to accuracies of a few parts per million. Meters usingamplifiers can measure tiny voltages of microvolts or less.
Part of the problem of making an accurate voltmeter is that of calibration to check its accuracy. In laboratories, the Weston Cell is used as a standard voltage for precision work. Precision voltage references are available based on electronic circuits.

Contents

  [hide] 
  • 1 Analog voltmeter
  • 2 VTVMs and FET-VMs
  • 3 Digital voltmeter
  • 4 See also
  • 5 References

Analog voltmeter[edit]

A moving coil galvanometer of thed'Arsonval type.
  • The red wire carries the current to be measured.
  • The restoring spring is shown ingreen.
  • N and S are the north and south poles of the magnet.
A moving coil galvanometer can be used as a voltmeter by inserting a high-resistance resistor in series with the instrument. It employs a small coil of fine wire suspended in a strong magnetic field. When an electric current is applied, the galvanometer's indicator rotates and compresses a small spring. The angular rotation is proportional to the current through the coil. For use as a voltmeter, a series resistor is added so that the angular rotation becomes proportional to the applied voltage.
One of the design objectives of the instrument is to disturb the circuit as little as possible and so the instrument should draw a minimum of current to operate. This is achieved by using a sensitive galvanometer in series with a high resistance.
The sensitivity of such a meter can be expressed as "ohms per volt", the number of ohms resistance in the meter circuit divided by the full scale measured value. For example a meter with a sensitivity of 1000 ohms per volt would draw 1 milliampere at full scale voltage; if the full scale was 200 volts, the resistance at the instrument's terminals would be 200,000 ohms and at full scale the meter would draw 1 milliampere from the circuit under test. For multi-range instruments, the input resistance varies as the instrument is switched to different ranges.
Moving-coil instruments with a permanent-magnet field respond only to direct current. Measurement of AC voltage requires a rectifier in the circuit so that the coil deflects in only one direction. Moving-coil instruments are also made with the zero position in the middle of the scale instead of at one end; these are useful if the voltage reverses its polarity.
Voltmeters operating on the electrostatic principle use the mutual repulsion between two charged plates to deflect a pointer attached to a spring. Meters of this type draw negligible current but are sensitive to voltages over about 100 volts and work with either alternating or direct current.

VTVMs and FET-VMs[edit]

The sensitivity and input resistance of a voltmeter can be increased if the current required to deflect the meter pointer is supplied by an amplifier and power supply instead of by the circuit under test. The electronic amplifier between input and meter gives two benefits; a rugged moving coil instrument can be used, since its sensitivity need not be high, and the input resistance can be made high, reducing the current drawn from the circuit under test. Amplified voltmeters often have an input resistance of 1, 10, or 20 megohms which is independent of the range selected. A once-popular form of this instrument used a vacuum tube in the amplifier circuit and so was called the vacuum tube voltmeter, or VTVM. These were almost always powered by the local AC line current and so were not particularly portable. Today these circuits use a solid-state amplifier using field-effect transistors, hence FET-VM, and appear in handheld digital multimeters as well as in bench and laboratory instruments. These are now so ubiquitous that they have largely replaced non-amplified multimeters except in the least expensive price ranges.
Most VTVMs and FET-VMs handle DC voltage, AC voltage, and resistance measurements; modern FET-VMs add current measurements and often other functions as well. A specialized form of the VTVM or FET-VM is the AC voltmeter. These instruments are optimized for measuring AC voltage. They have much wider bandwidth and better sensitivity than a typical multifunction device.

Digital voltmeter[edit]

Two digital voltmeters. Note the 40 microvolt difference between the two measurements, an offset of 34 parts per million.
The first digital voltmeter was invented and produced by Andrew Kay of Non-Linear Systems (and later founder of Kaypro) in 1954.
Digital voltmeters (DVMs) are usually designed around a special type of analog-to-digital converter called an integrating converter. Voltmeter accuracy is affected by many factors, including temperature and supply voltage variations. To ensure that a digital voltmeter's reading is within the manufacturer's specified tolerances, they should be periodically calibrated against a voltage standard such as the Weston cell.
Digital voltmeters necessarily have input amplifiers, and, like vacuum tube voltmeters, generally have a constant input resistance of 10 megohms regardless of set measurement range.

See also[edit]

  • Electrical measurements
  • Electrometer
  • Electronic test equipment
  • Metrology
  • Multimeter
  • Ohmmeter
  • Potentiometer (measuring instrument)
  • Solenoid voltmeter
  • Voltage divider
  • Class of accuracy in electrical measurements