A slightly long explanation of resistance.

• Ohm’s Law
• Resistance
• Factors affecting resistance
• Joule Heating

Let’s go!

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What is Ohm’s Law?
“For a conductor at a constant temperature, current through it is proportional to the potential difference across it.”
V ∝ I
V = Ik

The proportionality constant is what we label as resistance (R), giving us:
V = IR

Ohm’s Law isn’t really a LAW, because it is NOT always true.

In some materials, Ohm’s Law is true. These are OHMIC conductors	Plotting current against potential difference gives us this graph:
In other materials. Ohm’s Law is NOT true. These are NON-OHMIC conductors	Plotting current against potential difference gives us these graphs: Or

We will explore these graphs in the next post. For now, let’s answer a more basic question:

What is resistance?
Ratio of the potential difference across the conductor to the current in it.
R = V/I

It is measured in Ohms (Ω).
1Ω = 1V/A

That’s just rearranging V = IR. What does R mean really?
Resistance is the potential difference needed to drive 1A of current through a conductor. This can be used to measure how conductive or insulative a material is: the higher the potential difference needed to drive 1A of current through, the less conductive it is.

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What causes resistance?
Explaining this requires a deeper dive into how electrons work. Let’s take it step by step.

How do electrons behave in atoms?
See my post on electrons to explore how they really exist in atoms.
Electrons exist in orbitals (NOT orbits) around a nucleus – higher orbitals have higher energy levels. If an electron is given enough energy, it leaves the atom altogether (the atom is ionised).

How does this determine the conductivity of a material?

• In insulators, the electrons mostly stay bound to their atom since a VERY high energy is needed for them to leave.
• In a metal conductor, the electron is now free to move. Since metals are a lattice of positive ions, the electrons move by “jumping” from one ion to another. The better the conductor, the easier it is for electrons to do so.

If there is no electric field applied to a conductor, the electrons move randomly at all times.

Now, what if we apply an electric field?
If there is an electric field applied (say, the conductor is connected to positive & negative battery terminals), the electrons will move in a net direction. There is STILL RANDOM MOTION, but now they have an overall DRIFT to them! If the electric field is STRONGER, they will drift FASTER. To make the field stronger, you need a higher potential difference!

However, the motion of electrons in a general direction can be restricted by a few things:

• The type of material: the properties of the atoms & molecules inside a material may cause the electrons to travel easily or with difficulty
  • Impurities in a metal’s lattice act as ‘obstacles’ – areas where the electrons cannot travel as quickly
  • When electrons ‘collide’ with particles, they transfer some of their kinetic energy to those particles, heating them up
• The shape of the wire:
  • thicker wires have more electrons in total, allowing a higher current to flow through (this is the A in the I = nAvq)
  • longer wires actually decrease the drift speed, because the electrons are more likely to encounter ‘obstacles’ (decreasing the v in I = nAvq)
• The temperature of the wire: we will dicuss this in the next section

A material with a higher resistance would require a higher potential difference to create the same current.

Equation describing resistance:
R = ρL/A

ρ = resistivity (specific to the type of material), measured in Ωm^-1
L = length, measured in m
A = cross-sectional area, measured in m²

As we’ve discussed above:

• ρ: the higher the resistivity, the higher the resistance – R is proportional to ρ
• L: the longer the wire, the higher the resistance – R is proportional to L
• A: the thicker the wire, the lower the resistance – R is inversely proportional to A

How does heat affect resistance?
It can either INCREASE or DECREASE the resistance of a material – depending on the type of material.

Heat is basically the random motion of particles. If electrons are trying to flow through a material, having more random motion can either impede their flow (in conductors) OR make it easier (in some semiconductors). Let’s look at each case:

Conductors (metals)

Heat INCREASES resistivity & resistance. In metals, most valence electrons are already free to move around & flow. Adding heat causes the atoms to vibrate more, increasing the number of ‘collisions’ with electrons. Thus, it is difficult for the electrons to flow.

Certain semiconductors

Heat DECREASES resistivity & resistance. In insulators, very few valence electrons are free to move around & flow. Adding heat causes the atoms to vibrate more, giving more energy to the electrons & allowing them to escape their atom. This increases the number of free electrons, making it easier for electrons to flow.   Although the collisions still occur, the higher number of free electrons outweighs the effect for certain materials. Materials that exhibit this property are used as NTC thermistors!

Note: electron flow is also affected by their own random motion – AKA their heat! The hotter the electrons, the more random their motion, & the less they are able to travel in a single average direction. However, this effect is not discussed for A-Levels, so I’ll leave it out.

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What are the effects of resistance in a device?
A major effect is HEATING.

How does resistance cause heating?
Remember this fact from above: when electrons ‘collide’ with particles, they transfer some of their kinetic energy to those particles, heating them up.

Note: To say that they ‘collide’ is a little misleading – electrons actually transfer some of their kinetic energy to other particles by interacting with their electric & magnetic fields. If you move a magnet really fast near another magnet, the other magnet will gain a bit of speed!
However, ALL collisions are just like this: when you kick a ball, the atoms in your feet & the ball never touch – they are simply interacting with each other’s electric fields. So, I guess we CAN say they collide.

This effect is known as Joule Heating.

How do you quantitively measure the heat dissipated through Joule Heating?
The energy dissipated as heat per unit time is given as power:
P = VI

Since V=IR, we can also express P as:
P = I²R
P = V²/R

This is where the electric potential energy goes as electrons move across a resistor: it is transformed to heat! It is this heat that we utilise in many devices:

• Lightbulbs: heat causes the filament to glow, converting some heat energy into light
• Heaters: the heating device can be used to boil water or air

Sometimes, we say this heat is WASTEFUL – especially when we don’t want our device to lose any energy or give off heat. This is why we try to minimise the power loss in the transmission cables which supply electricity in our homes!