Here are some units used in physics.
Light can be measured in two ways: as irradiance or illuminance. The difference is that irradiance measures the power of electromagnetic radiation regardless of wavelength (radiometric unit), while illuminance weights visible wavelengths higher (photometric unit). The weighting factor is called the luminance function.
Luminance Function: Black traces: photopic (3 methods used to get 3 traces), green traces: scotopic. X-axis is wavelength (nm)
The luminance function weights wavelengths based on the sensitivity of the human eye. There are two commonly used functions: the photopic function (black traces in the graph) is the one commonly used when calculating light intensity in photometric units; and the scotopic function (green trace), which is used for very low light intensities. At low light intensities, the eye uses rods rather than the cones, and the sensitivity spectrum shifts towards the violet.
There are several methods used to calculate the photopic function, indicated by the 3 black traces. The solid line is the one used most often, and it represents the CIE 1931 color space.
Luminous Intensity: is a measure of the intensity (power) of a light source in a given direction. Since this is basically a measure of power, if a radiometric unit were used it would simply be watts. However, since this is being defined in photometric units, the wavelength of the light needs to be considered.
Historically, the unit of luminous intensity was candlepower, with one candlepower being the light produced by a standard candle - a candle made of pure spermaceti, weighing 1/6 of a pound, and burning at the rate of 120 grains per hour.
A new definition was proposed in 1979, and the unit was changed to candela. The new definition is: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 Hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
The 1/683 number was chosen so the Candela would be roughly the same as the older unit Candlepower. The frequency chosen corresponds to a wavelength of about 555 nm, which corresponds to the peak of the photopic luminance function.
Luminous Flux: is a measure of the perceived intensity of a source of light. This is similar to luminous intensity, but differs in that it is the total light emitted by the light source, whereas the luminous intensity is the light emitted per unit angle (in the case of a candela, per steradian). If a light source emits one candela in a particular direction over an angle of 1 steradian, then its luminous flux in that direction is 1 lumen. If we assume an isotropic light source (emitting uniformly in all directions) with an intensity of 1 candela, then its total luminance is 4*pi lumens.
Luminance: is a measure of the density of luminous flux in a given direction. It is similar to luminous flux, but measured in area rather than spherical angle. The unit is candela per square meter, sometimes termed nit (1 nit = 1 candela/m2). This unit is frequently used in the video industry to measure the brightness of monitors or screens. In lumens, a nit would be pi lumens per square meter. In CGS units, 1 lumen per square centimeter is called 1 lambert. Therefore a lambert would be (100 * 100)/pi = 3183.099 candelas per square meter, or 3183.099 nits.
Illuminance: is a measure of the total luminous flux incident on a surface per unit area. It measures how brightly a surface is illuminated. If one lumen of luminous flux covers an area of 1 square meter, then the illuminance of that area is 1 lux. In the CGS system, the unit is phot (1 phot = 10,000 lux). This is the unit that is most directly relevant to eye, determining how bright or dark a given scene or object appears to us. The human eye can see over a 2 trillion fold range of illuminance, from about 5x10-5 lux to 108 lux.
|0.00005 lux||50 ulx (microlux)||starlight|
|0.0001 lux||100 ulx||moonless overcast night sky|
|0.001 lux||1 mlx (millilux)||moonless clear night sky|
|0.01 lux||10 mlx||quarter moon|
|0.25 lux||250 mlx||full moon on a clear night|
|1 lux||1 lx||moonlight at high altitude in tropics|
|3 lux||3 lx||dark limit of twilight in clear sky|
|50 lux||50 lx||average living room|
|80 lux||80 lx||average hallway, toilet|
|400 lux||4 hlx (hectalux)||brightly lit office|
|400 lux||4 hlx||sunrise or sunset with clear sky|
|1,000 lux||1 klx (kilolux)||studio lighting|
|32,000 lux||32 klx||sunlight on average day (min)|
|100,000 lux||100 klx||sunlight on average day (max)|
Here are some typical conversion factors:
- 1 lumen = 1/683 watts = 0.00146 watts
- 1 candela steradian = 1 lumen
- 1 candela spherical (1 candlepower) = 1/(4*pi) = 0.07958 lumens
- 1 lumen/cm2 = 1 lambert
- 1 candela/m2 = 1 nit
- 1 lumen/m2 = 1/pi nits = 0.31831 nits
- 1 lambert = 1 lumen/cm2 = 0.31831 * 10000 = 3183.1 nits = 3183.1 candela/m2
- 1 foot candle = 1 lumen/foot2 = 1 foot lambert
- 1 foot candle = 1/10.76391 meter candle = 1/10.76391 lux
- 1 lux = 1/10000 phot
Logically, the basic unit in electricity should be charge. Other units, such as current, voltage, resistivity, etc. are concerned with things that happen to charges. However, in practice, this is not so, because some measurements are easier to make than others.
Charge: The fundamental charge is the charge of an electron or proton. All charges in the real world are some multiple of that. The charge of an electron is very small, about 1.602176487x10-19 coulombs. This could be used to define the coulomb, the unit of charge by saying that a coulomb is the combined charge of 6.24151×1018 electrons. These numbers are too large and impractical to be useful, but they do relate a unit of measurement to something fundamental in physics.
Another unit that could be derived similarly is a faraday, which is not much in use today. A faraday is the charge of one mole of electrons, which is about 96,485.3 coulombs.
The accepted definition of coulomb in the SI system is based on the current, which is measured in amperes. If a current of 1 ampere flows between two points every second, then the amount of charge flowing across those points per second is 1 coulomb.
Current: is the amount of charge flowing between two points per second. The SI unit for current is ampere and is defined as follows: the constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in a vacuum, would produce between these conductors a force equal to 2×10–7 newton per meter of length.
Voltage: also known as potential difference, is the difference in electrical potential between two points. A difference in electrical potential may be defined as the amount of work a unit charge is capable of doing when moving from one point to the other. Another way to think of it is that there is a charge imbalance between the two points. Imagine you have two identical spheres. One has a surplus of electrons (and is therefore negatively charged), while the other has a deficit (and is therefore positively charged). There is a charge imbalance between the two, and if current were allowed to flow (for example, if they are connected by a copper wire), then current will flow between them. By convention we say that charge is flowing from the more positive terminal to the more negative terminal, though in actual fact in this case the movement of electrons is from the negative end to the positive end. This makes no difference, it is simply a matter of choosing a + or - sign by convention, and then sticking to it.
|Silver||1.59 x 10-8|
|Copper||1.72 x 10-8|
|Gold||2.44 x 10-8|
|Aluminum||2.82 x 10-8|
|Tungsten||5.60 x 10-8|
|Nickel||6.99 x 10-8|
|Carbon||3.50 x 10-5|
|Silicon||6.40 x 10-2|
|Germanium||4.60 x 10-1|
|Teflon||1022 - 1024|
As mentioned above, a difference in electrical potential may be defined as the amount of work a unit charge is capable of doing when moving from one point to the other. It is useful to look at it the other way - the amount of work done that would be needed to move the charge against the electrical potential. In other words, if we have two points, A and B, and electrons move under the influence of this difference in potential from A to B, then we can say that the potential difference is:
- the amount of work an electron can do when it flows from A to B, OR
- the amount of work it would take to move the electron against the electrical potential from B to A.
The two quantities are identical. In this case, we are using a single electron as a unit of charge to illustrate. Since by convention current flows from positive to negative, while electrons flow the opposite way, the second case above is more useful. The unit of potential difference is the volt, and it is defined as follows: if one ampere of current is flowing between two points, and it takes 1 joule of energy is to move this amount of charge per second, then the potential difference across the two points is 1 volt. Alternatively, we can say that if 1 ampere of current is flowing between the points and 1 joule of energy is dissipated per second (energy that could have done 1 joule of work), then the potential difference across the two points is 1 volt. Since 1 joule per second = 1 watt, we can also say that if 1 ampere of current flows between 2 points and the energy dissipated is 1 watt, then the potential difference between the two points is 1 volt. Finally, translating current back to charge, if a charge of 1 coulomb moving between points A and B is capable of doing 1 joule of work per second, then the potential difference between A and B is 1 volt.
Resistance: is a measure of how much a material opposes the flow of current through it. Assuming a current of constant density, resistance would be proportional to the length of the resistor and inversely proportional to its cross section.
The unit of resistance or impedance (in the case of AC) is the ohm in the SI system. An ohm is defined as the resistance of a conductor in which a current of 1 ampere is produced by a potential difference of 1 volt across its ends. The reciprocal of resistance is conductance, and is measured in siemens. The difference between resistivity and resistance is that resistivity is simply a characteristic of the medium through which the current flows, while resistance depends on resistivity plus a number of other factors, such as the shape and dimensions of the medium. Resistivity (and consequently resistance) increases with the temperature; therefore the specific resistivity of a material has to be defined at a given temperature.
It's important to note that these simple explanations apply only to DC. In the case of AC, the situation is more complex, because of the skin effect (current density being higher at the surface of the conductor than at the core). Also, conductors that are near each other (such as bundles of wires) have higher resistance than lone conductors. For these reasons, another measure of resistance is used for AC, known as impedance. Impedance is also measured in ohms, but it includes both the resistance and the reactance (a complex number based on the amplitude and phase of the AC).
Capacitance: is a measure of the amount of charge stored (or separated) for a given electrical potential. To understand this, let's consider the example of a simple capacitor, which is simply two plates called electrodes, separated by a medium called the dielectric (the medium might be air or vacuum, or anything else).
The plates can be connected to a battery, with one plate being connected to the positive terminal of the battery and the other to the negative terminal. This causes a buildup of charges (positive on one, negative on the other) on the two plates. The amount of charge will obviously depend upon the voltage of the battery - the higher the voltage (or potential difference it can apply across its terminals), the greater the charge that will build up on the plates.
Capacitance is the ability of the plates to hold larger and larger amounts of charges, for the same applied potential difference. Therefore, two plates which develop a certain charge when "X" amount of potential difference is applied have more capacitance than another set of plates that can develop the same amount of charge only when "2X" the amount of current is applied. Therefore, capacitance is inversely proportional to the potential difference, and directly proportional to the amount of charge that can be stored.
Capacitance depends on a number of factors, such as the area of the plates (the larger the area, i.e., the larger the capacitor, the more the charge it can hold), the material of the capacitor, and the nature of the dielectric between them.
The dielectric could be anything: a solid, a gas such as air, or even vacuum. However, charge tends to leak across the gap between the plates, in air or vacuum, so the presence of a material with high relative static permittivity (high dielectric constant) can impede this charge leakage, and increase the capacity of the plates. Commonly used dielectrics are paper, glass, plastic, mica and ceramics.
The unit of capacitance is the farad. If a potential difference of 1 volt across a capacitor results in the storage (or separation) of 1 coulomb of charge between the two electrodes, then the capacity is 1 farad.
Some uses for Capacitors:
Because of their ability to store energy, they are used as temporary batteries to maintain power supply while the main batteries are being changed.
They are used in power conditioning, to smooth out the output of rectifiers, which convert DC to AC. They are also widely used in electronics such as audio amplifiers to remove the AC "hum" and similar cyclic variations in current.
The energy stored in capacitors can be treated as information (charged state = 1, discharged state = 0), as in DRAM memory, CCDs (charge coupled devices), etc.
They can be used in tuned circuits, where they select particular frequencies (such as in radio receivers to select a particular carrier wave for a certain station). Usually, the capacitance combined with the inductance (LC) is used to tune radios.
Since the capacitance depends on the area of the plates, the distance between them, and the dielectric, changes in any of these things can be used to sense the physical environment. For example, detecting changes in the dielectric to detect changes in the humidity of air, changes in distance between plates to sense changes in fuel level in aircraft fuel tanks, or changes in area of the plates in capacitive touch switches. If the plates are flexible, deformation of the plates in any way will change the capacitance of the circuit, which is used in condenser microphones.
Capacitor banks can be used to provide pulsed power in applications where large pulses of current are needed, such as pulsed lasers, weapon systems, fusion research, etc.
Since capacitors allow AC current but prevent the flow of DC current, they can be used to separate AC from DC signals.
The opposite of capacitance is elastance (simply the reciprocal of capacitance), and is measured in units called darafs.
Although typically capacitance is thought of as a charge separation between two adjacent electrodes, it's possible to think of a single electrode as having self-capacitance. This is typically done for spheres (such as those used in van de Graaf generators to store charge), and is defined as the amount of charge that needs to be added to the sphere to raise its potential by 1 volt. When we say "raise its potential", implicit in the statement is the question "in reference to what?" The reference here is a theoretical hollow conducting sphere of infinite radius, with the electrode being measured placed at its center. The self-capacitance of the typical van de Graaf sphere (20 cm radius) is 20 picofarads, while the self-capacitance of the Earth is about 710 microfarads.