In this article, we will cover:
- What is Resistance?
- Ohm's Law
- How the Shape of a Conductor Affects Resistance
- Resistivity and Conductivity
- How Temperature Affects Resistivity
- Are Water, Air, and Vacuums Insulators or Conductors?
What is Resistance?
Free electrons in a metal wire at room temperature undergo collisions between themselves, positive lattice ions, and impurities within the material. These collisions impede the free electron's forward motion and so reduce the magnitude of the current. We associate these mechanisms with electrical resistance.
Ohm's Law
R = V/I where R is resistance (measured in ohms), V is voltage (measured in volts) and I is current.
Ohm's Law is not actually a law, more of a statement of the observed behavior of materials. Materials that follow Ohm's Law (materials where resistance is constant) are called ohmic materials and those that do not are called nonohmic materials.
Note: It is important to note that just because Ohm's Law is written as V = IR does not mean that R is in any way related to voltage. For example, when the voltage across a material increases, its resistance does not increase. Resistance is defined in terms of current and voltage, but voltage is not defined in terms of resistance and current. V = IR can still be used to find the voltage across a component given its current and resistance, but, again, its current that increases with voltage, resistance is constant.
How the Shape of a Conductor Affects Resistance
If you increase the length of a conductor, its resistance increases. This is because the free electrons have to undergo a higher number of collisions as the distance they must travel to get to their destination is larger and there are more free electrons in the wire to collide with (because, linking to a water analogy, the pipe is always full).
If you increase the cross-sectional area of the wire, its resistance decreases. This is because a thicker wire can support a higher current flow. Thus, if you keep current constant (between a thin and thick wire), there is a lower current density, so there are less collisions between free electrons and other free electrons (and positive lattice ions and impurities). This means a lower applied electric field is required to allow the same amount of current to flow. Hence, drift velocity is smaller in thicker wires too.
Resistivity and Conductivity
Resistivity is the resistance of a substance with a cross-sectional area of 1 m^2 and a length of 1 m. This means that resistivity is a property unique to the material and not dependent of length or area. If you want to compare the overall resistance of a brass wire to that of a copper wire, you could use the resistivity value.
The equation for resistivity is as follows:
resistivity = (resistance x cross-sectional area)/length
Resistivity is measured in ohm-metres (Ωm)
Conductivity is the inverse of resistivity. It shows you how good a substance is at passing current. It is measured in Siemens.
This equation for conductivity is:
conductivity = 1/resistivity
How Temperature Affects Resistivity
Resistivity (and conductivity) are both temperature-dependent. In most materials, as temperature increases, resistivity increases. This is because, as temperature increases, positive lattice ions, free electrons, and impurities, vibrate more, increasing collisions and reducing the drift velocity of the free electrons.
The following equation links temperature change with the resulting change in resistivity. Alpha represents the temperature coefficient of resistivity (units are 1/(degrees Celcius)). p0 and T0 is the reference resistivity and the reference temperature respectively.
Are Water, Air, and Vacuums, Insulators or Conductors?
Water - Distilled water is a very good insulator because there are very few charge carriers within it. Water autoionisation can give rise to a positive ion (H3O+) and a negative ion (OH-). They are attracted to a negative electrode and a positive anode respectively. When they reach the electrode, they either gain or lose an electron, then recombine to form H2O. Whilst this does mean that distilled water can technically conduct electricity, this autoionisation process only produces 1 or 2 ions per 10 million H20 atoms. As well as this, many of the ions recombine before reaching the electrodes anyway.
Saltwater - Saltwater is a much better conductor than distilled water because there is a lot of sodium chloride dissolved with it. This compound ionises into Na+ and Cl- ions which are free to carry charge.
Human Skin - Varies with moisture and salt content. Is a reasonably good insulator.
Air - Is an insulator because it is considered to be quite void of free electrons. However, ionisation can take place where an electron is knocked free from and N2 or O2 molecule. This makes polar molecules (like water) attract to the new ion. This cluster of particles is known as a positive air ion. The free electron usually attaches itself to a O2 molecule, making a negative ion. Hence, air is considered to be neutral. If you apply a very strong electric field across air (using two plates), it can be possible to accelerate the free electrons so they produce more ion pairs. Three scenarios then may occur:
Corona discharge- Only the air immediately around the conductor has a high enough breakdown field strength (a field strength capable of causing free electrons to create more ion pairs) so ionisation occurs immediately around the conductor but no further. Everywhere else in the field, there is only a current of very slow-moving ions and free electrons moving to their applicable plate.
Spark discharge - Between two well-rounded conductors with different potentials (where one is usually grounded), like corona discharge ionisation starts at a point of breakdown field strength, but in spark discharge these ionisations occur all the way between the electrodes.
Brush discharge - In between the corona and spark discharges. Can occur between a charged material and a grounded conductor with some curvature. Almost all discharges from insulators are brush discharges.
Vacuum - Considered to be a perfect insulator because there are no free charges at all. However, the 4 special processes mentioned in the "Microscopic View of Conduction Article" can free electrons from a surface into the vacuum, thus creating free charges.
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