Current and the Ampere

Definition:

The electrical current is defined as the amount of charge that passes per unit time through an area perpendicular to the flow.

If the flow is constant,

I=	Q

	t

When the current varies with time, we have to use calculus to define the current. The current I is the rate of flow (i.e. the time derivative) of the charge:

I=	dQ

	dt

Non-calculus version of this statement:

I=	$\Delta$Q

	$\Delta$t

in the limit of very small $\Delta$t

Units:

From the definition:

[I] = [Q] / [t] = C/s (Coulomb per second)

In honor of Andre Ampere (1775-1836) this unit is named the Ampere (A)

1 A =	1 C

	1 s

In the international system of units, the SI is one of the base-units, i.e. a unit that cannot be derived from other units. Then the Coulomb is a derived unit defined as: 1 C = 1 A $\cdot$ 1 s.

Convention for the direction of the current:

The direction of the current is defined as the direction of the positive charge flow. In metal wires, however, only the electrons actually move, so the conventional direction of the current is opposite to the direction of the flow of charges (electrons). Current is a scalar.

How many electrons flow per second in a current of 1 A? Since q_e = 1.6$\cdot$10^-19 C, There are 1 / 1.6$\cdot$10^-19 = 6.3$\cdot$10¹⁸ electrons per Coulomb. So 1 A consists of that very large number of electrons per second crossing a surface.