# ampere

##### SI base unit
Name Symbol Quantity
ampere A electric current

### Definition

The ampere, symbol A, is the SI base unit of electric current.

The ampere is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 × 10−19 when expressed in the unit C, which is equal to s A, where the second is defined in terms of ΔνCs.

The definition of the ampere implies the exact relation e = 1.602 176 634 × 10−19 s A. Inverting this relation gives an exact expression for the unit ampere in terms of the defining constants e and ΔνCs :

$1 \mspace{4mu} \text{A} \mspace{10mu} = \dfrac{e}{1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19}} \mspace{6mu} \text{s}{^{-1}}\\ \\ \\ 1 \mspace{4mu} \text{A} \mspace{10mu} = \dfrac{1}{(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})} \mspace{6mu} \Delta \nu _{Cs} \mspace{6mu} e\\ \\ \\ 1 \mspace{4mu} \text{A} \mspace{10mu} = 6.789 \mspace{4mu} 686 \mspace{4mu} 817 \mspace{4mu} 250 \mspace{4mu} 553 \mspace{4mu} 926 \text{...} \times 10^{8} \mspace{6mu} \Delta \nu _{Cs} \mspace{6mu} e$

The effect of this definition is that one ampere is the electric current corresponding to the flow of 11.602 176 634 × 10–19 elementary charges per second.

The ampere is named after the French mathematician and physicist André-Marie Ampère (1775 – 1836).

### Electric current

An electric current, I, is the rate of flow of electric charge, Q, past a given point in a given time, t.

$I \ = \ \dfrac{Q}{t}$

The SI unit of charge, the coulomb, synbol C, is the amount of electric charge carried in one second by a current of one ampere. Conversely, a current of one ampere is one coulomb of charge passing a given point in one second:

$1 \ \text{A} = 1 \ \dfrac{\text{C}}{\text{s}}$

An electric current consists of the movement of particles called charge carriers.

• In a metal wire, charge is carried by the loosely bound electrons of metal atoms.
• In an electrolyte, charge is carried by ions (charged atoms or molecules).
• In an ionised gas, or plasma, charge is carried by ions and electrons.

### Ohm’s law

An electric current, I, flows between two points of a conductor when a potential difference, or voltage, V, is applied across the two points.

Ohm’s law states that the current, I, through a conductor between two points is directly proportional to the voltage, V, across the two points. The current is also indirectly proportional to the resistance of the conductor.

$I \propto \dfrac{V}{R}$

Using SI coherent units, the proportionality constant is 1, Thus:

$I \ = \dfrac{V}{R}$

where:

• current, I, is measured in amperes, symbol A,
• voltage, V, is measured in volts, symbol V,
• resistance, R, is measured in ohms, symbol Ω.

$1 \ \text{A} = 1 \ \dfrac{\text{V}}{\Omega}$

### Joule’s first law

Joule heating, also known as resistive heating, is the process of heat dissipation by which the passage of an electric current through a conductor increases the internal energy of the conductor, converting thermodynamic work into heat. Joule’s first law states that the rate of heat production, or resistive heating power P, of a conductor is directly proportional to the product of the square of the current I and its electrical resistance R.

$P \propto I^2 R$

Using SI coherent units, the proportionality constant is 1, Thus:

$P = I^2 R$

where

• power, P, is measured in watts, symbol W,
• current, I, is measured in amperes, symbol A,
• resistance, R, is measured in ohms, symbol Ω.

$1 \ \text{W} \mspace{4mu} = 1 \ \text{A}^2 \ \Omega$

Resistive heating is utilised in incandescent light bulbs and electric fires.

### Electromagnetism

Electric current produces a magnetic field. The magnetic field can be visualised as a pattern of circular field lines surrounding the wire.

In an electromagnet, a current passing through a coil of wire produces a magnetic field with a pattern of field lines resembling those of a permanent magnet. The magnetic field produced by an electric current persists only as long as there is current.

### Electromagnetic induction

Magnetic fields can also be used to make electric currents. When a changing magnetic field is applied to a conductor, an electromotive force (EMF) is induced, which starts an electric current, when there is a suitable path.