Resistors, Capacitors, and Inductors 24310.1 Resistors
Resistance is associated with the phenomenon of energy
dissipation. In its simplest form, it is a measure of the
opposition to the flow of current by a piece of electric
material. Resistance dissipates energy in the form of
heat; the best conductors have low resistance and
produce little heat, whereas the poorest conductors have
high resistance and produce the most heat. For example,
if a current of 10 A flowed through a resistance of 1:,
the heat would be 100 W. If the same current flowed
through 100:, the heat would be 10,000 W, which is
found with the equation
(10-1)where,
P is the power in watts,
I is the current in amperes,
R is the resistance in ohms.
In a pure resistance—i.e. one without inductance or
capacitance—the voltage and current phase relation-
ship remains the same. In this case the voltage drop
across the resistor is
(10-2)where,
V is the voltage in volts,
I is the current in amperes,
R is the resistance in ohms.
All resistors have one by-product in common when
put into a circuit, they produce heat because power is
dissipated any time a voltage, V, is impressed across a
resistance R. This power is calculated from Eq. 10-1 or
(10-3)where,
P is the power in watts,
V is the voltage in volts,
R is the resistance in ohms.
Changing the voltage, while holding the resistance
constant, changes the power by the square of the
voltage. For instance, a voltage change from 10 V to
12 V increases the power 44%. Changing the voltage
from 10 V to 20 V increases the power 400%.
Changing the current while holding the resistance
constant has the same effect as a voltage change.
Changing the current from 1 A to 1.2 A increases the
power 44%, whereas changing from 1 A to 2 A
increases the power 400%.
Changing the resistance while holding the voltage
constant changes the power linearly. If the resistance is
decreased from 1 k: to 800: and the voltage remains
the same, the power will increase 20%. If the resistance
is increased from 500: to 1 k:, the power will
decrease 50%. Note that an increase in resistance causes
a decrease in power.
Changing the resistance while holding the current
constant is also a linear power change. In this example,
increasing the resistance from 1 k: to 1.2 k: increases
the power 20%, whereas increasing the resistance from
1k: to 2 k: increases the power 100%.
It is important in sizing resistors to take into account
changes in voltage or current. If the resistor remains
constant and voltage is increased, current also increases
linearly. This is determined by using Ohm’s Law, Eq.
10-1 or 10-3.
Resistors can be fixed or variable, have tolerances
from 0.5% to 20%, and power ranges from 0.1 W to
hundreds of watts10.1.1 Resistor CharacteristicsResistors will change value as a result of applied
voltage, power, ambient temperature, frequency change,
mechanical shock, or humidity.
The values of the resistor are either printed on the
resistor, as in power resistors, or are color coded on the
resistor, Fig. 10-1. While many of the resistors in
Fig. 10-1 are obsolete, they are still found in grandma’s
old radio you are asked to repair.Voltage Coefficient. The voltage coefficient is the rate
of change of resistance due to an applied voltage, given
in percent parts per million per volt (%ppm/V). For
most resistors the voltage coefficient is negative—that
is, the resistance decreases as the voltage increases.
However, some semiconductor devices increase in resis-
tance with applied voltage. The voltage coefficient of
very high valued carbon-film resistors is rather large
and for wirewound resistors is usually negligible. Va r i s -
tors are resistive devices designed to have a large
voltage coefficient.Temperature Coefficient of Resistance. The tempera-
ture coefficient of resistance (TCR) is the rate of change
in resistance with ambient temperature, usually stated as
parts per million per degree Celsius (ppm/°C). Many
types of resistors increase in value as the temperature
increases, while others, particularly hot-molded carbon
types, have a maximum or minimum in their resistancePI=^2 RVIR=P V2R----- -=