Electricity Basics: Resistance, Inductance & Capacitance
Several examples of resistors. Resistors convert energy to heat and dissipate it.
Credit: Peter Mathys, University of Colorado

Electronic circuits are integral parts of nearly all of the technological advancement in our lives today. Television, radio, phones and computers immediately come to mind, but electronics are also used in automobiles, kitchen appliances, medical equipment and industrial controls. At the heart of these devices are semiconductors — transistors, diodes and triodes. However, these devices could not function without much simpler components that predate semiconductors by many decades. These include resistors, capacitors and inductors. 

As its name implies, a resistor is an electronic component that resists the flow of electric current in a circuit. Electrical resistance is analogous to friction in a mechanical system. They both convert energy to heat and dissipate it to the surrounding environment, so electrical resistance can sometimes be thought of as a braking or damping mechanism in a circuit. 

In metals such as silver or copper, which have high electrical conductivity and therefore low resistivity, electrons are able to skip freely from the conduction band of one atom to the next, encountering little resistance. However, in a material such as carbon, electrons encounter numerous collisions that make it more difficult for them to move through the material, according to Serif Uran, a professor of physics at Pittsburg State University. Insulators such as glass have extremely high resistivity, with virtually no spaces in their conduction bands that would allow electrons to move through them. 

The electrical resistance of a circuit component is defined as the ratio of the applied voltage to the electric current that flows through it, according to HyperPhysics. The standard unit for resistance is the ohm, which is named after German physicist Georg Simon Ohm. It is defined as the resistance in a circuit with a current of one ampere at one volt. Resistance can be calculated using Ohm's Law, which states that resistance equals voltage divided by current, or R = V/I, where R is resistance, V is voltage and I is current. Ohm's Law is more commonly written as the equivalent expression V = IR. One way to understand Ohm's Law is to hold one of these variables constant, change the value of another variable, and watch what happens to the third variable. For instance, if we keep voltage constant and increase the resistance, the current must decrease. If we keep the resistance constant and increase the voltage, the current must increase. 

Resistors are generally classified as either fixed or variable. Fixed-value resistors are simple passive components that always have the same resistance within their prescribed current and voltage limits. They are available in a wide range of resistance values from less than 1 ohm to several million ohms with tolerances ranging from plus or minus 0.1 percent to plus or minus 10 percent. Resistors are also classified by the maximum voltage they can tolerate as well as the maximum amount of power they can dissipate. 

The resistance of a simple resistor can be calculated as R = ρL/A, where R is resistance, L is its length, A is its cross-sectional area and ρ is resistivity, which is an inherent property of the material. Resistivity is the reciprocal of conductivity σ, i.e., ρ = 1/σ. All other things being equal, a resistor that is twice as long will have twice the resistance, and one with twice the cross-sectional areal will have half the resistance. Also, material with higher resistivity will result in proportionally greater resistance. 

Variable resistors are simple electro-mechanical devices, such as volume controls and dimmer switches, which increase the effective length of a resistor by turning a knob or moving a slide control. Strain gauges are resistors in which resistance changes with strain. Strain occurs when an object is stretched or compressed. A thermistor is a temperature sensor. It changes resistance when an increase in temperature excites electrons, making them available to conduct current, thus reducing the resistivity of the material. A piezoresistor changes its resistivity in response to a change in strain, which causes more or fewer electrons to be available to carry charge. 

An inductor is an electronic component consisting simply of a coil of wire. A constant electric current running through an inductor produces a magnetic field. If the current changes, so does the magnetic field. The unit for inductance is the henry (H), named after Joseph Henry, an American physicist who discovered inductance independently at about the same time as English physicist Michael Faraday. One henry is the amount of inductance that is required to induce one volt of electromotive force when the current is changing at one ampere per second. 

Oersted’s Law, named after Danish physicist Hans Christian Oersted, states that a constant electric current generates a magnetic field around the conductor. Faraday’s Law of Induction states that a changing magnetic field induces a current in a conductor within that field. Finally, Lenz's law, named after Russian physicist Heinrich Lenz, states that this induced current is in the opposite direction of the change in current that produced the magnetic field. This phenomenon is called self-inductance. 

What this means is, if you quickly reduce the current through the inductor, the changing magnetic field will induce a current that opposes the change, which tends to maintain the current at its previous level. Conversely, if you increase the current sharply, the induced current will be in the opposite direction of the increase, which again tends to maintain the current at a constant level. In other words, an inductor creates a kind of inertia in the current flow that resists rapid changes in much the same way that a massive body resists changes in its velocity. 

One important application of inductors in active circuits is that they tend to block high-frequency signals while letting lower-frequency oscillations pass. Note that this is the opposite function of capacitors. Combining the two components in a circuit can selectively filter or generate oscillations of almost any desired frequency. 

With the advent of integrated circuits, inductors are becoming less common because three-dimensional coils are extremely difficult to fabricate in two-dimensional layers produced by thin-film lithography. For this reason, microcircuits are designed to avoid using inductors, and instead use capacitors to achieve essentially the same results, according to Michael Dubson, a professor of physics at the University of Colorado Boulder. 

Several examples of capacitors. Capacitors store electric charge.
Several examples of capacitors. Capacitors store electric charge.
Credit: Peter Mathys, University of Colorado

Capacitance is the ability of a device to store electric charge. An electronic component that stores electric charge is called a capacitor. The earliest example of a capacitor is the Leyden jar. This device was invented to store a static electric charge on conducting foil used to line the inside and outside of a glass jar.  

The simplest capacitor consists of two flat conducting plates separated by a small gap. The potential difference, or voltage, between the plates is proportional to the difference in the amount of the charge on the plates. This is expressed as Q = CV, where Q is charge, V is voltage and C is capacitance. 

The capacitance of a capacitor is the amount of charge it can store per unit of voltage. The unit for measuring capacitance is the farad (F), named for Faraday, and is defined as the capacity to store one coulomb of charge with an applied potential of one volt. One coulomb (C) is the amount of charge transferred by a current of one ampere in one second. 

In practice, it would take a huge capacitor to store one coulomb of charge at one volt. The capacitance of a simple parallel-plate capacitor is equal to the permittivity of free space times the area of the plates divided by the distance between them, or C = ε0A/d, where C is the capacitance, A is the area of the plates, d is the separation between the plates, and ε0 (epsilon naught) is the permittivity of free space which is equal to 8.58 × 10−12 F/m. 

A one-farad capacitor made of two flat metal plates with 1 mm of air space between them would be about 113 square kilometers (43.6 square miles). Fortunately, there are better ways to make capacitors that are much more space-efficient than this. In practice, plates are stacked in layers or wound in coils and spaced much more closely than 1 mm. They also use dielectric materials between the plates that work much better than an air gap. Dielectrics are insulating materials that allow for close spacing between the plates, and they partially block the electric field between the plates in proportion to their dielectric constant, which is a measure of the material's relative permittivity compared to that of free space. This allows the plates to store more charge without arcing and shorting out. Interestingly, for a transparent material, such as glass or diamond, its dielectric constant is essentially the same as its refractive index which is the ratio the of speed of light in vacuum (c) to the speed of light in that material. 

Capacitors used in electronic circuits are typically measured in microfarads (μF), nanofarads (nF) and picofarads (pF), which are millionths, billionths and trillionths of a farad, respectively. However, larger capacities can be achieved using thin film deposition to produce dielectric layers that are only a few atoms thick. 

Capacitors are often found in active electronic circuits that use oscillating electric signals such as those in radios and audio equipment. They can charge and discharge nearly instantaneously, which allows them to be used to produce or filter certain frequencies in circuits. An oscillating signal can charge one plate of the capacitor while the other plate discharges, and then when the current is reversed, it will charge the other plate while the first plate discharges. In general, higher frequencies can pass through the capacitor, while lower frequencies are blocked. The size of the capacitor determines the cut-off frequency for which signals are blocked and which are allowed to pass. Capacitors in combination can be used to filter selected frequencies within a specified range. 

Supercapacitors are manufactured using nanotechnology to create super-thin layers of materials such as graphene to achieve capacities that are 10 to 100 times that of conventional capacitors of the same size; however, they have much slower response times than conventional dielectric capacitors, so they cannot be used in active circuits. Compared to batteries, though, these devices have extremely fast charging times, and they can withstand thousands of charging cycles. Their main disadvantage is that they are considerably larger than batteries for the same amount of stored energy. Also, supercapacitors can only operate at low voltages, generally less than four volts; however, like battery cells, they can be connected in series to provide higher voltages. 

Inductors, resistors and capacitors are often combined in what are commonly called RLC circuits to generate or receive oscillating signals of specific frequencies. Interestingly, their behavior can be modeled using the exact same mathematics as for simple harmonic motion of a damped mass–spring system. In this case, the resistance R is analogous to friction; the inductance L is analogous to the mass; and the capacitance C is analogous to the spring constant. In both cases, the system will have one specific resonant frequency at which it will naturally tend to oscillate. 

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