handbook of modern sensors

3.5 Resistance 59
Fig. 3.16. Voltage across a material sets the electric
current.
3.5 Resistance
In any material, electrons move randomly like gas in a closed container. There is
no preferred direction and an average concentration of electrons in any part of the
material is uniform (assuming that the material is homogeneous). Let us take a bar of
an arbitrary material. The length of the bar is l. When the ends of the bar are connected
to the battery having voltage V (Fig. 3.16), an electric field E will be setup within the
material. It is easy to determine the strength of the electric field:
E = V l
(3.49)
For instance, if the bar has a length of 1 m and the battery delivers 1.5 V, the electric
field has a strength of 1.5 V/m. The field acts on free electrons and sets them in motion
against the direction of the field. Thus, the electric current starts flowing through the
material. We can imagine a cross section of the material through which passes electric
charge q. The rate of the electric charge flowing (unit of charge per unit of time) is
called the electric current:
i = dq
(3.50)
dt
The SI unit of current is ampere (A): 1 A = 1 coulomb/sec. In SI units, ampere
is defined as the electric current maintained in two infinitely long parallel wires
separated by 1minfree space, which produce a force between the two wires (due
to their magnetic field) of 2 × 10 −7 N for each meter of length. An ampere is quite
strong electric current. In sensor technologies, generally much smaller currents are
used; therefore, submultiples of A are often employed:
1 milliampere (mA): 10 −3 A
1 microampere (µA): 10 −6 A
1 nanoampere (nA): 10 −9 A
1 picoampere (pA): 10 −12 A
1 femtoampere (fA): 10 −15 A
Regardless of the cross section of the material, whether it is homogeneous or not,
the electric current through any cross section is always the same for a given electric
field. It is similar to water flow through a combination of serially connected pipes of