Electrical current is the rate of flow of charge.

$$ I = \frac{\Delta Q}{\Delta t} $$

If the current is constant this simplifies to

$$ Q = It $$

This very important.

It is very important to understand that one of the most definitive laws of physics is the conservation of charge. This has strong implications for the way we analyse the flow of current in circuits.

So, if 10 C flows in 2 minutes the current id given by

$$ I = \frac{10}{2 \times 60} $$

$$ I = 0.083 A \; ( 83 mA )$$

The charge carriers in metals are free electrons - conduction electrons. Conduction electrons are freed from the metallica atoms and are free to move throughout the metallic crystal solid. They are also partly responsible for the conduction of heat through the metal.

In insulators there are very few free electrons.

In semiconductors energy releases more charge carriers. This can happen by suppling energy in the form of heat, light or electrical energy. Semiconductors have two charge carries, electrons and holes.

Holes are positive as they are effectively the gaps produced when electrons are freed from covalent bonds.

One way to measure the ability of a material to conduct electricity is to measure the number of free charge carriers per unit volume of the material.

Metals have a charge density of about \( 5 \times 10^{28} \) electrons per cubic meter.

Silver has an electron density of \( 5.69 \times 10^{28} \).

So if we assume the electrons have a drift velocity of \( v_{drift} \) then the current flowing in a wire cross-sectional area A is

$$ I = nAv_{drift}e $$

So given \( A = \pi(0.2 \times 10^{-3})^2 \)

$$ I = 5.69 \times 10^{28} \times \pi(0.2 \times 10^{-3})^2 \times v_{drift} \times 1.6 \times 10^{-19} $$

so for a current of 25 mA

$$ v_{drift} = 0.31 ms^{-1} $$

A beam of electrons is passed across a vacuum tube.

If the electrons travel at \( 2 \times 10^5 ms^{-1} \) how many electrons have passed through the tube in 1 second if the current is \( 25 \mu A \)?

$$ = \frac {2 \times 10^5}{1.6 \times 10^{-19}} $$

$$ = 1.25 \times 10^{24} $$

electrons per second