### 2.02 Electrical current (i)

Electrical current is a measure of the rate of flow of electrical charge through a material. Consider an electrical current flowing through a wire. The magnitude of the electrical current will depend on

• The number density of mobile charge carriers within the material. (the greater the number of free charge carriers that are available within the material the greater the current will be.)  • The amount of charge carried by each of the charge carriers. (the greater the amount of charge carried by each of the charge carriers the greater the current will be.)   (Note in solid materials the charge carriers are electrons so the charge is simply the charge carried by an electron 1.6 x 10-19C)

• The drift velocity at which the electrons move along the wire. (The faster the electrons travel the greater the current will be).  • The cross sectional area of the wire. (the larger the cross sectional area across which the electrons flow the larger the current will be)  I = naqv

• I is the current measured in Amps (A)
• n is the number density measured in mobile charge carriers per cubic metre (m-3)
• a is the cross sectional area of the material measured in metres squared (m2)
• q is the amount of charge carried by each of the mobile charge carriers measured in Coulombs (C)
• v is the drift velocity of the charge carriers in metres per second (ms-1)

Example

• a wire has a number density of 2x1028m-3
• the cross sectional area of the wire is 2.5 mm2
• the charge carriers are electrons so the charge on each carrier is 1.6 x 10-19 C
• the drift velocity of the free electrons is 1mms-1

I   =   naqv   =    2x1028m  x   2.5x10-6  x   1.6 x 10-19  x   1x 10-3    =   8 Amps

Note the symbol q represents the amount of charge carried by the mobile charge carriers within the material. If the material is a liquid or gas the charge carriers could be positive or negative ions as well as electrons. The charge on ions can vary depending on the level of ionisation. In solid materials the only charge carriers which are free to move are electrons. The charge on an electron is fixed (1.6 x 10-19 C). Because we are often dealing with solid conductors the symbol q is sometimes replaced by the symbol e to represent the charge on the electron.

I = nave

As well as replacing q by e, the right hand side of the equation has been rearranged to make it easier to remember. As the values on the right hand side of the equation are multiplied together it does not matter which way round we write them