Resistors, Capacitors, and Inductors 247Resistors in Parallel. The total resistance of resistors
in parallel is(10-7)If two resistors are in parallel use:(10-8)When all of the resistors are equal, divide the value
of one resistor by the number of resistors to determine
the total resistance. The total resistance is always less
than the smallest resistor.
To determine the value of one of the resistors when
two are in parallel and the total resistance and one
resistor in known, use(10-9)10.1.3 Types of ResistorsEvery material that conducts electrical current has resis-
tivity, which is defined as the resistance of a material to
electric current. Resistivity is normally defined as the
resistance, in ohms, of a 1 cm per side cube of the mate-
rial measured from one surface of the cube to the oppo-
site surface. The measurement is stated in ohms per
centimeter cubed (:/cm^3 ). The inverse of resistivity is
conductivity. Good conductors have low resistivity, and
good insulators have high resistivity. Resistivity is
important because it shows the difference between
materials and their opposition to current, making it
possible for resistor manufacturers to offer products
with the same resistance but differing electrical, phys-
ical, mechanical, or thermal features.
Following is the resistivity of various materials:
Carbon-Composition Resistors. Carbon-composition
resistors are the least expensive resistors and are widely
used in circuits that are not critical to input noise and do
not require tolerances better than r5%.
The carbon-composition, hot-molded version is basi-
cally the same product it was more than 50 years ago.
Both the hot- and cold-molded versions are made from
a mixture of carbon and a clay binder. In some versions,
the composition is applied to a ceramic core or arma-
ture, while in the inexpensive version, the composition
is a monolithic rigid structure. Carbon-composition
resistors may be from 1: to many megohms and
0.1–4 W. The most common power rating is ¼ W and
½ W with resistance values from 2:–22 M:.
Carbon-composition resistors can withstand higher
surge currents than carbon-film resistors. Resistance
values, however, are subject to change upon absorption
of moisture and increase rapidly at temperatures much
above 60°C (140°F). Noise also becomes a factor when
carbon-composition resistors are used in audio and
communication applications. A carbon-core resistor, for
example, generates electrical noise that can reduce the
readability of a signal or even mask it completely.Carbon-Film Resistors. Carbon-film resistors are
leaded ceramic cores with thin films of carbon applied.
Carbon film resistors offer closer tolerances and better
temperature coefficients than carbon composition resis-
tors. Most characteristics are virtually identical for
many general purpose, noncritical applications where
high reliability, surge currents, or noise are not crucial
factors.Metal Film Resistors. Metal film resistors are discrete
devices formed by depositing metal or metal oxide films
on an insulated core. The metals are usually either
nichrome sputtered on ceramic or tin oxide on ceramic
or glass. Another method of production is to screen or
paint powdered metal and powdered glass that is mixed
in an ink or pastelike substance on a porous ceramic
substrate. Firing or heating in an oven bonds the mate-
rials together. This type of resistor technology is called
cermet technology.
Metal film resistors are most common in the 10:to
1M: range and^1 e 8 W to 1 W with tolerances of r1%.
The TCR is in the r100 ppm/°C range for all three
technologies. Yet there are subtle differences:- Cermet covers a wider resistance range and handles
higher power than nichrome deposition. - Nichrome is generally preferred over tin oxide in the
upper and lower resistance ranges and can provide
TCRs that are lower than 50 ppm/°C. - Tin oxide is better able to stand higher power dissipa-
tion than nichrome.
Material Resistivity
Aluminum 0.0000028
Copper 0.0000017
Nichrome 0.0001080
Carbon (varies) 0.0001850
Ceramic (typical) 100,000,000,000,000 or (10^14 )RT^1
1
R 1----- -^1
R 2----- - } 1
Rn++----- -= ----------------------------------------RTR 1 uR 2
R 1 +R 2= ------------------R 2RTuR 1
R 1 – RT=------------------