Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 286

11.7.9.5 Resistivity
All materials differ in their atomic structure and therefore in their ability to resist the flow of an
electric current. The measure of the ability of a specific material to resist the flow of electricity
is called its resistivity or speciic resistance —the resistance in ohms offered by unit volume (the
circular-mil-foot) of a substance to the flow of electric current. Resistivity is the reciprocal of con-
ductivity (i.e., the ease with which current flows in a conductor). A substance that has a high resistiv-
ity will have a low conductivity, and vice versa .
The resistance of a given length for any conductor depends on the resistivity of the material, the
length of the wire, and the cross-sectional area of the wire according to the following equation:

L
A

R =ρ (11.43)

where
R = Resistance of the conductor (ohms).
ρ = Specific resistance or resistivity (circular mil ohm/ft).
L = Length of the wire (ft).
A = Cross-sectional area of the wire (circular mil).

The factor ρ (Greek letter rho) permits different materials to be compared for resistance according
to their nature without regard to different lengths or areas. Higher values of ρ mean more resistance.

Key Point: The resistivity of a substance is the resistance of a unit volume of that substance.

11.7.10 m agnetiC u nits
The law of current flow in the electric circuit is similar to the law for the establishing of flux in the
magnetic circuit. The magnetic flux (ϕ, phi) is similar to current in the Ohm's law formula and is the
total number of lines of force existing in the magnetic circuit. The Maxwell (Ma) is the unit of flux;
that is, 1 line of force is equal to 1 Maxwell.

Note: The Maxwell is often referred to as simply a line of force , line of induction , or line .

The strength of a magnetic field in a coil of wire depends on how much current flows in the turns
of the coil—the more current, the stronger the magnetic field. In addition, the more turns, the more
concentrated are the lines of force. The force that produces the flux in the magnetic circuit (compa-
rable to electromotive force in Ohm's law) is known as magnetomotive force (mmf). The practical
unit of magnetomotive force is the ampere-turn (At). In equation form,

F (ampere-turns) = N × I (11.4 4)

where
F = Magnetomotive force (At).
N = Number of turns.
I = Current (A).

■ EXAMPLE 11.46
Problem: Calculate the ampere-turns for a coil with 2000 turns and a 5-Ma current.

Solution: Use Equation 11.44 and substitute N = 2000 and I = 5 × 10 -3 A:

N × I = 2000 × (5 × 10 -3 ) = 10 At