Conduction and Resistance

Electrical Quantities

Define conduction in metals.

The movement of delocalised electrons through a metal, producing an electric current.

Why can metals conduct electricity?

They contain delocalised electrons that are free to move through the metal lattice.

Describe the structure of a metal.

A regular lattice of positive metal ions surrounded by delocalised electrons.

What are delocalised electrons?

Electrons that are no longer associated with one particular atom and are free to move through the metal.

What happens to conduction electrons when no potential difference is applied?

They move randomly due to thermal motion, so there is no net movement of charge.

Why does random electron motion not produce a current?

The electrons move randomly in all directions, so there is no overall movement of charge in one direction.

What happens when a potential difference is applied across a metal?

An electric field is established, causing the free electrons to have an overall drift through the metal.

In which direction do electrons drift in a metal?

Towards the positive terminal.

In which direction is conventional current?

From the positive terminal to the negative terminal.

How does electron flow compare with conventional current?

Electrons drift in the opposite direction to conventional current.

Define drift velocity.

The average overall velocity of charge carriers through a conductor due to an applied electric field.

Do electrons stop moving randomly when a potential difference is applied?

No. Their slow drift motion is superimposed on their rapid random thermal motion.

How does the random thermal speed of electrons compare with their drift velocity?

Random thermal speeds can be thousands of kilometres per second, while drift velocity is usually only millimetres per second.

Why is drift velocity much smaller than the random speed of electrons?

Electrons undergo frequent collisions with the metal lattice, continually changing direction.

What is the transport equation?

I = nAvq.

What does I represent in I = nAvq?

Current in amperes (A).

What does n represent in I = nAvq?

Number density of charge carriers in m⁻³.

What does A represent in I = nAvq?

Cross-sectional area of the conductor in m².

What does v represent in I = nAvq?

Drift velocity of the charge carriers in m s⁻¹.

What does q represent in I = nAvq?

Charge on each charge carrier in coulombs (C).

What is the magnitude of the charge on an electron?

1.60 × 10⁻¹⁹ C.

What is the actual charge of an electron?

−1.60 × 10⁻¹⁹ C.

What equation can be used to calculate drift velocity?

v = I/(nAq).

What equation can be used to calculate number density?

n = I/(Avq).

What equation can be used to calculate cross-sectional area using the transport equation?

A = I/(nvq).

What equation can be used to calculate the charge on a charge carrier using the transport equation?

q = I/(nAv).

Define number density.

The number of charge carriers per unit volume of a material.

What is the unit of number density?

m⁻³.

How is the cross-sectional area of a circular wire calculated?

A = πr².

How is radius calculated from the diameter of a wire?

r = d/2.

What happens to drift velocity if current increases while n, A and q remain constant?

Drift velocity increases.

What happens to drift velocity if the cross-sectional area increases while current remains constant?

Drift velocity decreases.

What happens to drift velocity if the number density of charge carriers increases for the same current and area?

Drift velocity decreases.

Why does a thinner wire have a greater drift velocity for the same current?

A smaller cross-sectional area means the charge carriers must drift faster to carry the same amount of charge per second.

How can the transport equation be derived from the definition of current?

Start with I = ΔQ/Δt and consider the charge passing through a cross-section of conductor in time Δt.

How far do charge carriers drift in a time Δt?

Δx = vΔt.

What volume of conductor passes a cross-section in time Δt?

V = AΔx = AvΔt.

How many charge carriers are contained in the volume AvΔt?

N = nAvΔt.

What charge passes through the cross-section in time Δt?

ΔQ = nAvqΔt.

How does ΔQ = nAvqΔt lead to the transport equation?

Substitute it into I = ΔQ/Δt, giving I = nAvq.

What causes electrical resistance in a metal?

Collisions between conduction electrons and the fixed ions of the metal lattice.

What happens to an electron when it collides with a lattice ion?

Its direction of motion changes and energy can be transferred to the lattice.

Why does a longer wire have a greater resistance?

Electrons travel through more lattice and undergo more collisions.

How does increasing the temperature of a metal affect its lattice ions?

The ions vibrate with greater amplitude.

Why does increasing temperature increase the resistance of a metal?

More strongly vibrating lattice ions cause more frequent collisions with conduction electrons, reducing their drift velocity for a given electric field.

How does the resistivity of a typical metal change as temperature increases?

It increases.

Why does the resistivity of metals increase with temperature?

Increased lattice vibrations cause more collisions between conduction electrons and ions.

What happens when a larger current passes through a filament lamp?

The filament becomes hotter.

Why does the resistance of a filament lamp increase as current increases?

The increased current heats the filament, causing greater lattice vibrations and more electron-ion collisions.

Why does the I–V graph of a filament lamp flatten at high voltages?

Higher current heats the filament, increasing its resistance, so current increases less rapidly with voltage.

How does temperature affect the number density of charge carriers in a metal?

It decreases slightly because the metal thermally expands.

Why is the change in number density of a metal with temperature usually not the main effect?

The increase in electron-lattice collisions is much more significant.

How does the behaviour of semiconductors differ from metals as temperature increases?

The number of available charge carriers in a semiconductor increases significantly.

How does the resistivity of a semiconductor change as temperature increases?

It decreases.

Why does semiconductor resistivity decrease with increasing temperature?

More charge carriers become available for conduction, increasing conductivity.

How does conductivity of a semiconductor change with temperature?

It increases as temperature increases.

How does conductivity of a typical metal change with temperature?

It decreases as temperature increases.

What is the key difference between resistance and resistivity?

Resistance depends on the material and dimensions of a component, whereas resistivity is a property of the material.

Why should resistance and resistivity not be confused?

Resistance describes a particular component, while resistivity describes the material from which it is made.

What is the relationship between current and drift velocity according to the transport equation?

For constant n, A and q, current is directly proportional to drift velocity.

If drift velocity doubles and everything else remains constant, what happens to current?

The current doubles.

If the cross-sectional area doubles at constant drift velocity, what happens to current?

The current doubles.

If number density doubles while A, v and q stay constant, what happens to current?

The current doubles.

Why can an electrical signal travel quickly even though electron drift velocity is slow?

The electric field is established throughout the circuit very quickly; individual electrons only need to drift slowly.