Inductive
reactance
Electrical resistance is not the only property of materials
that resists the flow of current. Let us consider an
experiment. Let’s purchase a 12,000-foot spool of insulated
20 AWG copper wire commonly used as communications wire and
pull the wire off the spool and lay it out on the ground. If
we take the two ends and connect them to a male electrical
plug and plug it into a 120 V AC source, we would expect the
current magnitude that would flow in the wire to be equal to
the source voltage divided by the resistance of the wire.
Since the resistance of 20 AWG copper wire is 10.1 W / 1000 ft at a temperature of 20°C,
then 12,000 feet would have a resistance 12 x 10.1 or 121.2 W.
From Ohm’s law, the current we would expect to see would be
the voltage divided by the resistance, 120 / 121.2 = 0.9900
amp. If we take the same wire and wrap it tightly around a
4-inch diameter solid rod of iron and then energize it from
the 120-volt source, as before, we would find that the current
is considerably less. If the current is less, then the
resistance must have increased. If the current is now 0.7682
amp, the resistance must now be equal to the voltage divided
by the current or 120 / 0.7682 = 156.21 W.
How did the resistance increase from 121.2 to 156.21? It didn’t.
By wrapping the wire around the iron rod, we introduced
another form of resistance to current flow into the circuit.
This second form is called inductive reactance.
Inductive reactance is created any time we wrap wire in a
coil. The current in the coiled wire creates a magnetic field
around the coil. The inductive reactance is particularly high
when the space inside the coil is filled with iron. Electrical
resistance in a conductor resists the flow of current by
generating heat. Inductive reactance resists the flow of
current by generating a magnetic field. The symbol we use in
calculations to represent inductive reactance is XL. The
unit of measure is the same as for electrical resistance, the
ohm symbolized by W.
Impedance
In our voltage-drop calculations we performed as part of this
series of articles, to calculate the current in the circuit,
we divided the source voltage by the total resistance in the
circuit. The total resistance in the circuit was the sum of
the resistance of each element of the circuit, the service
wire, the wire within the house, the extension cord, and the
load. Resistance elements that are in series can be added to
determine the total resistance. When we deal with resistance
and inductive reactance in the same circuit, the current in
the circuit is the source voltage divided by the total
impedance. Impedance is used in place of total resistance
because what impedes the flow of current is a combination of
resistance and inductive reactance. The term impedance is also used because resistance and inductive reactance cannot
be added together. For calculation purposes, the symbol for
impedance is Z. To calculate the total impedance, we have to
refer to what we call the impedance triangle. Resistance forms
one side of the triangle, inductive reactance forms the other
side of the triangle, and the total impedance is the
hypotenuse. The Pythagorean theorem covers the relationship
between resistance, inductive reactance, and impedance; the
square of the hypotenuse is equal to the sum of the squares of
the other two sides. Z2 = R2 + XL2 If we solve for Z we get:
Z = square root (R2 + XL2)
In our experiment, we found the impedance
of the 12,000 feet of wire wrapped around the iron rod is
equal to the source voltage divided by the current, 120 /
0.7682 = 156.21 W.
Since the resistance of the wire is 121.2 W,
and the total impedance of the wire is 156.21 W,
the inductive reactance must be:
XL = square root (Z2 – R2)
XL = 98.54 W
Electric Motors
In general, the amount of power consumed by an electric motor
is a function of the rated horsepower of the motor and how
much mechanical load is placed on the motor. A motor with 100
percent efficiency would draw 746 watts of power for every
horsepower of mechanical load placed on the motor. A motor
with a more realistic efficiency of 80 percent would draw
almost 900 watts of power for every horsepower of mechanical
load placed on it. When motors run without load, they draw
anywhere from 30% to 70% of their full load power. When motors
are first energized, some draw several times their full load
power in the form of a current surge until the motor is up to
speed. For example, my hand-held circular saw draws 22 amps
for about a second when it is first turned on. After the
initial surge of current, it draws 9 amps. When I’m cutting
through a 4 by 4 of treated lumber, it draws 13 amps. In
general, electric motors have high levels of inductive
reactance because the magnetic field is a very important part
of motors. When my saw is cutting through the 4 by 4, the
resistance of the saw is 7.384 W
and the inductive reactance 5.538 W.
The total impedance is:
Z = square root (R2 + XL2)
Z = 9.23 W
Power
When we looked at conductors and loads with little or no
inductive reactance, we only considered the resistance, and we
calculated the power consumed by the resistance by multiplying
the voltage across the resistance times the current flowing
through the resistance. Now that we are looking at a load that
has both resistance and inductive reactance, we have to
consider other forms of power. The power associated with the
heat generated by current flowing through a resistance is
called real power. It is calculated as we did before by
multiplying the voltage across the resistance times the
current flowing through the resistance. The symbol for real
power is P. The unit of measure is watt. The abbreviation for
watt is W. The power associated with inductive reactance,
which maintains the magnetic field within the motor, is called reactive power. The symbol for reactive power is Q. The
unit of measure is var. There is no abbreviation. The
combination of real power and reactive power is called apparent
power. The symbol for apparent power is S. The unit of
measure is volt-amperes. The abbreviation is VA. To calculate
the apparent power, we have to refer to what we call the power
triangle. Real power forms one side of the triangle, reactive
power forms the other side of the triangle, and the apparent
power is the hypotenuse. The Pythagorean theorem covers the
relationship between real power, reactive power, and apparent
power; the square of the hypotenuse is equal to the sum of the
squares of the other two sides. S2 = P2 + Q2. If we solve for S we get:
S = square root (P2 + Q2)
The apparent power can also be calculated
by multiplying the voltage times the current. For my saw, the
apparent power is 120 x 13 = 1560 VA. The real power is I2 x R or 13 x 13 x 7.384 = 1248 W. The reactive power is I2 x XL or 13 x 13 x 5.538 = 935.9 var. The term power
factor is commonly used to measure how much inductive
reactance is in a load. Power factor is abbreviated PF and is
calculated by dividing the real power by the apparent power.
For my saw, the PF is 1248 / 1560 = 0.8, commonly referred to
as 80% power factor. Another way of calculating PF is to
divide the load resistance by the load impedance. For my saw,
the PF is 7.384 / 9.23 = 0.80 or 80%.
Please send me your comments on this
series. If you have questions about basic electricity or
general questions about the NESC, please e-mail me at dave.young@conectiv.com .
National Electrical Safety Code and NESC
are registered trademarks of the Institute of Electrical and
Electronics Engineers. National Electrical Code and NEC
are registered trademarks of the National Fire Protection
Association.
Dave is a consulting engineer with Conectiv Power
Delivery of Wilmington, Delaware, where he has been working with and
teaching all aspects of the NESC for over 33 years. He is a member of
the NESC Interpretations Subcommittee and represents the Edison Electric
Institute on the NESC Overhead Line Clearances Subcommittee 4. Dave is
also an inspector member of the IAEI. |
