# Voltage, Current, Resistance, Capacitance

Submitted by jan on Tue, 01/22/2019 - 17:39

To understand how neurons process information, it is necessary to be familiar with some very basic notions of electronics, in particular those of voltage, current, resistance, and, to a lesser extent, capacitance. If you are not sure you know exactly what these terms mean, then reviewing the following may be helpful:

## Electric charge

The "stuff" all around us, as well as the stuff that we are made from, is made out of molecules, and molecules are made of atoms, and atoms are made of fundamental particles including electrons (which make up the "shell" of atoms) and protons (which are part of the atom's core, or "nucleus"). Electrons and protons are said to carry "electric charge". This electric charge comes in two different types. The charge of a proton is arbitrarily referred to as "positive", that of an electron is said to be "negative".  For historical reasons, the charge of 6.242×1018 protons is said to be "1 Coulomb" worth of charge, while the charge of  6.242×1018 electrons would be "minus 1 Coulomb".

The letter Q serves as symbol for electric charge in physical equations, and the letter C serves for the abbreviation for the SI unit of charge, Coulomb.

## Electrostatic forces

Electrical phenomena all stem from the basic observation that objects carrying charges of the same type (same "sign") repel each other, while those of opposite sign attract each other. The strength of the attraction or repulsion between two charged objects depends on how much charge there is on the objects, as well as on the distance between the objects. The mathematical formula that relates the strength of the attractive or repulsive force to charge and distance is known as "Coulomb's law".  Coulomb's law is a type of "inverse square law", because the size of the force is inversely related to the square of the distance. So halving the distance increases the force by one over half squared, i.e. four fold. Decreasing the distance by a quarter increases the force sixteen fold. You can imagine that, as you bring charges very close together, the forces can become very large indeed, and conversely if you separate charges by a large distance, the forces can become negligibly small. The notion of an  "electric field" describes the possible electrostatic forces that a charge, or a number of charges, would create in the space around them.

## Ions

Normally in an atom or in a molecule made up of atoms, the number of protons in the nuclei is equal to the number of electrons in the shell and the atom is therefore said to be "electrically neutral" because the attraction or repulsion that a charge outside the atom may experience toward the atom's electrons will be cancelled out by the opposite force it will experience toward the atom's protons. However, some atoms are often found in configurations when the number of electrons is smaller or larger than the number of protons. The difference is usually not much, typically just one or at most two electrons. Atoms or molecules in which the number of electrons is not equal to the number of protons are called "ions". They are not electrically neutral because they have a "net charge" equal to the difference in the number of electrons and protons.

## Electric Potential Energy - Volts

If electrically charged particles, such as ions, are in an electric field, they will experience a  force, as just described, and that force will push or pull them, and may accelerate them according to Newton's laws of motion. If you allow a charged particle to be accelerated be an electric field, that particle will accumulate kinetic energy. Thus, the electric fields that are created by charge distributions are associated with a "electric potential energy", or just "electric potential" for short. An electric potential that is strong enough to exercise a force of one Newton on a charge equal to one Coulomb over the distance of one meter is said, by definition, to correspond to one Volt. Thus, you want to think of a "voltage" as a measure of how much potential energy is inherent in some distribution of charges in space as these charges can push or pull on other charges via electrostatic attraction. A popular analogy to make this more intuitive is to say that voltage does to electric charges something that is a bit like what hydrostatic pressure does to droplets of water. A lot of pressure can push hard on water droplets, and thereby make them do work, perhaps by pushing them through a water wheel or turbine.

The letter V serves both as symbol for "voltage" and as abbreviation for the unit Volts.

## Electric Current - Amperes

Whenever charged particles move about, one can speak of an "electric current". Of course if charges move around randomly and you get as many charges moving from, say, left to right as from right to left then the net distribution of charges doesn't change much, and we are therefore normally only interested in the "net movement" of charge, say how many more charges have moved from left to right that from right to left. Such coordinated movements of charge in a particular direction is to be expected if there are electric fields driving charges down a voltage gradient. The SI unit for electric current is the "Ampere", and one says that a current of one Ampere flows from A to B if one Coulomb worth of charge per second moves from A to B. Remember that one Coulomb corresponds to the charge of a very large number (6.242×1018) of elementary charged particles, so one Ampere is a lot of current, and in everyday life most electrical currents will be in the order of milliamps or less.

The letter I serves as symbol for electric current in physical equations, and the letter A serves for the abbreviation for the SI unit for current, the Ampere.

## Electric Resistance - Ohms

If electric charges are experiencing an electric field corresponding to some voltage, that field will push or pull on them and you might expect them to start moving down the field gradient, and an electric current will flow. However, that is only going to happen if these charges are actually able to move and aren't "stuck down" somehow. Materials in which electric charges cannot move even if voltages are applied to them are electrical insulators. Materials which allow electric charges to move if a voltage is applied are said to be electrical conductors. In neuroscience, the most common conductor we would come across are fluids in which ions are dissolved, and the ions can move about in the fluid. Of course, different materials may differ in how easily charges can move through them. Also, just having more of a particular material may make it easier for charges to move and electric currents to flow, if, for example more charged currents can flow side by side through a large opening rather than having to squeeze through some narrow opening one after the other. "Electrical resistance" measures how hard it is for charges to flow.

The letter R serves as symbol for electric resistance, and the Greek letter Ω serves for the abbreviation for the SI unit for resistance, the Ohm.

If a voltage of one Volt can drive a current of one Ampere through some piece of material, then the material is said to have an electrical resistance of one Ohm. If the resistance is smaller, the current created by a given voltage will be proportionally larger. If I want a big current to flow then I will want a large voltage driving the current and a small resistance. The proportionality relationship linking voltage, current and resistance is called "Ohm's law": I = V / R, or equivalently V=R ⋅ I .

Sometimes you may come across the term "conductance". A material that is a good conductor has high conductance and therefore low resistance. So conductance is simply the inverse of the resistance.  The SI unit of conductance is the "Siemens". 1 Siemens = 1 / Ohm.

## Electric Capacitance

Quite often in electronics, and even in neuroscience, may you encounter a situation where two materials that can conduct electric charges are found close together, but are separated by an insulator. Such configurations are known as a "capacitor", and they have important or interesting properties. Imagine you were to push some positive charge onto one of the two conductors. These charges would then create an electric field which might attract negative charges onto the the other conductor. If that happens, the attraction between the positive charges on one conductor of the capacitor and the negative charges on the other leads to a relatively stable configuration, where the charges are "held" in the capacitor by that electrostatic attraction. Capacitors which have large conductors (so that there is lots of room for charges) which are very close together, separated by only a very thin insulator (so that there can be strong attractive forces between the opposite charges on each conductor) are said to have a large "capacitance" because they can accommodate a lot of charge even if only a small voltage pushes the charges onto its conductors.

The letter C serves as symbol for electric capacitance, and the letter F serves for the abbreviation for the SI unit for resistance, the "Farad". A capacitor that can accommodate one Coulomb of charge if it is charged by a voltage of one Volt is said to have a capacitance of one Farad. The larger the capacitance, the more charge can be accommodated for a given voltage: C=Q/V.

The relationship between capacitance, voltage and charge also implies that, if I want to change the voltage between the two conductors of a large capacitor then I will need to move a lot of charge first. If I don't move charge then the electric field between the charges that already sit on the capacitor will maintain the voltage at the current level. In the context of neuroscience, that is an important detail because the cell membranes of neurons act like capacitors, and for neurons to do electrical signalling, the voltage across the membrane needs to change. The fact that cell membranes have capacitance means that voltage changes cannot happen infinitely quickly, effectively creating a "speed limit" for how quickly voltages can change and therefore ultimately how fast you can think.