E1C01 09/14/2010
15:40:35 Page 27
Many engineers have some difficulty with using g c in the non-SI systems. Actually, whenever
force and mass appear in the same expression, just remember to relate them using g c through
Newton’s law:
g c ¼
mg
F
¼ 1
kg À m/s
2
N
¼ 32:174
lb m À ft/s
2
lb
¼ 9:80665
kg À m/s
2
kg f
ð1:20Þ
Other Derived Dimensions and Units
Energy is defined as force times length and uses the unit of the joule (J), which is derived from base
units as
1 J ¼ 1
kg À m
2
s 2
¼ 1 N À m
ð1:21Þ
Power is defined as energy per unit time in terms of the unit of the watt (W), which is derived
from base units as:
1 W ¼ 1
kg À m
2
s 3
¼ 1
J
s
ð1:22Þ
Stress and pressure are defined as force per unit area, where area is length squared, in terms of
the pascal (Pa), which is derived from base units as
1 Pa ¼ 1
kg
m À s 2 ¼ 1 N/m
2
ð1:23Þ
Electrical Dimensions
The units for the dimensions of electrical potential, and resistance, charge, and capacitance are
based on the definitions of the absolute volt (V), and ohm (V), coulomb (C), and farad (F),
respectively. Derived from the ampere, 1 ohm absolute is defined by 0.9995 times the resistance to
current flow of a column of mercury that is 1.063 m in length and has a mass of 0.0144521 kg at
273.15 K. The volt is derived from the units for power and current, 1 V ¼ 1 N-m/s-A ¼ 1W/A. The
ohm is derived from the units for electrical potential and current, 1 V ¼ 1 kg-m
2 /s
3 -A
2
¼ 1 V/A. The
coulomb is derived from the units for current and time, 1 C ¼ 1 A-s. One volt is the difference of
potential between two points of an electical conductor when a current of 1 ampere flowing between
those points dissipates a power of 1 watt. The farad (F) is the standard unit for capacitance derived
from the units for charge and electric potential, 1 F ¼ 1 C/V.
On a practical level, working standards for resistance and capacitance take the form of certified
standard resistors and capacitors or resistance boxes and are used as standards for comparison in the
calibration of resistance measuring devices. The practical potential standard makes use of a standard
cell consisting of a saturated solution of cadmium sulfate. The potential difference of two
conductors connected across such a solution is set at 1.0183 V and at 293 K. The standard cell
maintains constant electromotive force over very long periods of time, provided that it is not
subjected to a current drain exceeding 100 mA for more than a few minutes. The standard cell is
typically used as a standard for comparison for voltage measurement devices.
1.5 Standards 27
15:40:35 Page 27
Many engineers have some difficulty with using g c in the non-SI systems. Actually, whenever
force and mass appear in the same expression, just remember to relate them using g c through
Newton’s law:
g c ¼
mg
F
¼ 1
kg À m/s
2
N
¼ 32:174
lb m À ft/s
2
lb
¼ 9:80665
kg À m/s
2
kg f
ð1:20Þ
Other Derived Dimensions and Units
Energy is defined as force times length and uses the unit of the joule (J), which is derived from base
units as
1 J ¼ 1
kg À m
2
s 2
¼ 1 N À m
ð1:21Þ
Power is defined as energy per unit time in terms of the unit of the watt (W), which is derived
from base units as:
1 W ¼ 1
kg À m
2
s 3
¼ 1
J
s
ð1:22Þ
Stress and pressure are defined as force per unit area, where area is length squared, in terms of
the pascal (Pa), which is derived from base units as
1 Pa ¼ 1
kg
m À s 2 ¼ 1 N/m
2
ð1:23Þ
Electrical Dimensions
The units for the dimensions of electrical potential, and resistance, charge, and capacitance are
based on the definitions of the absolute volt (V), and ohm (V), coulomb (C), and farad (F),
respectively. Derived from the ampere, 1 ohm absolute is defined by 0.9995 times the resistance to
current flow of a column of mercury that is 1.063 m in length and has a mass of 0.0144521 kg at
273.15 K. The volt is derived from the units for power and current, 1 V ¼ 1 N-m/s-A ¼ 1W/A. The
ohm is derived from the units for electrical potential and current, 1 V ¼ 1 kg-m
2 /s
3 -A
2
¼ 1 V/A. The
coulomb is derived from the units for current and time, 1 C ¼ 1 A-s. One volt is the difference of
potential between two points of an electical conductor when a current of 1 ampere flowing between
those points dissipates a power of 1 watt. The farad (F) is the standard unit for capacitance derived
from the units for charge and electric potential, 1 F ¼ 1 C/V.
On a practical level, working standards for resistance and capacitance take the form of certified
standard resistors and capacitors or resistance boxes and are used as standards for comparison in the
calibration of resistance measuring devices. The practical potential standard makes use of a standard
cell consisting of a saturated solution of cadmium sulfate. The potential difference of two
conductors connected across such a solution is set at 1.0183 V and at 293 K. The standard cell
maintains constant electromotive force over very long periods of time, provided that it is not
subjected to a current drain exceeding 100 mA for more than a few minutes. The standard cell is
typically used as a standard for comparison for voltage measurement devices.
1.5 Standards 27