To say that Ohm’s law is true for a particular conductor is
to say that the resistance of this conductor is, in fact, constant with respect
to current and voltage. Certain materials and electronic devices exhibit a
nonlinear relationship between current and voltage, that is, their resistance
varies depending on the voltage applied.

The relationship V = IR will still hold at any given time,
but the value of R will be a different one for different values of V and I.
These nonlinear devices have specialized applications and will not be discussed
in this chapter.

Resistance also tends to vary with temperature, though a
conductor can still obey Ohm’s law at any one temperature. For example, the
resistance of a copper wire increases as it heats up. In most operating
regimes, these variations are negligible.

Generally, in any situation where changes in resistance are
significant, this is explicitly mentioned. Thus, whenever one encounters the
term “resistance” without further elaboration, it is safe to assume that within
the given context, this resistance is a fixed, unchanging property of the
object in question.

Resistance depends on an object’s material composition as
well as its shape. For a wire, resistance increases with length, and decreases
with cross-sectional area. Again, the analogy to a gas or water pipe is handy:
we know that a pipe will allow a higher flow rate for the same pressure
difference if it has a greater diameter, while the flow rate will decrease with
the length of the pipe.

This is due to friction in the pipe, and in fact, an
analogous “friction” occurs when an electric current travels through a
material.

This friction can be explained by referring to the microscopic
movement of electrons or ions, and noting that they interact or collide with
other particles in the material as they go. The resulting forces tend to impede
the movement of the charge carriers and in effect limit the rate at which they
pass.

These forces vary for different materials because of the
different spatial arrangements of electrons and nuclei, and they determine the
material’s ability to conduct. This intrinsic material property, independent of
size or shape, is called resistivity and is denoted by r (the Greek lowercase
rho).

The actual resistance of an object is given by the
resistivity multiplied by the length of the object (l ) and divided by its
cross-sectional area (A): R = RHO X LENGTH/ AREA

The units of resistance are ohms, (Greek capital omega). By
rearranging Ohm’s law, we see that resistance equals voltage divided by
current. Units of resistance are thus equivalent to units of voltage divided by
units of current. By definition, one ohm equals one volt per ampere (OHM =
V/A).

The units of resistivity are ohm-meters (OHM-m), which can
be reconstructed through the preceding formula: when ohm-meters are multiplied
by meters (for l ) and divided by square meters, the result is simply ohms.

Resistivity, which is an intrinsic property of a material,
is not to be confused with the resistance per unit length (usually of a wire),
quoted in units of ohms per meter (oHM/m). The latter measure already takes
into account the wire diameter; it represents, in effect, the quantity rho/A.
The resistivities of different materials in V-m can be found in engineering
tables.

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