
Fill the appropriate dimensions for given quantity and complete the table.

Answer to Problem 1ICA
The completed table with appropriate dimension for given quantity is,
Dimensions | |||||||||
Quality | SI Units | M | L | T | N | J | I | ||
Example | Acoustic impedance | 1 | 0 | 0 | 0 | 0 | |||
(a) | Circuit resistance | 0 | 0 | 0 | |||||
(b) | Luminous efficiency | 3 | 0 | 0 | 1 | 0 | |||
(c) | Molar concentration | 0 | 0 | 0 | 1 | 0 | 0 | ||
(d) | Thermal conductivity | 1 | 1 | 0 | 0 | 0 |
Explanation of Solution
Given data:
The SI unit of circuit resistance is
The SI unit of luminous efficacy is
The SI unit of Molar concentration is
The SI unit of thermal conductivity is
Calculation:
Refer to the Table 9-1 in the textbook for Fundamental dimensions and base units.
Refer to the Table 8-1 in the textbook for Common derived units in the SI system to find the fundamental dimension of voltage.
Substitute M for kg, L for
Therefore, the dimensions of the voltage is
Find the fundamental dimension of resistance as follows.
Substitute
Therefore, the dimensions of the circuit resistance is
Find the fundamental dimension of luminous efficiency as follows.
Luminous efficacy is the measure of visible light produced by the source and is the ratio of luminous flux to power.
Fundamental dimension of luminous flux output (cd) is J.
Find the fundamental dimension of power.
Refer to the Table 8-14 in the textbook for Summary of electrical properties.
Substitute
Substitute J for cd and
Therefore, the dimensional formula of the luminous efficacy is
Consider the conversion factor to convert Liter to
Substitute
As the value
Substitute N for mol and
Therefore, the dimensional formula of the molar concentration is
Find the fundamental dimension of thermal conductivity.
Calories can be measured in units of Joules.
Refer to the Table 8-11 in the textbook for Dimension of energy to represent the dimensions of required parameters.
Substitute J for cal in equation (3) to find the thermal conductivity in terms of Joule.
Substitute
Obtained dimensions for circuit resistance, luminous efficacy and thermal conductivity is tabulated in Table 1.
Table 1
Dimensions | |||||||||
Quality | SI Units | M | L | T | N | J | I | ||
Example | Acoustic impedance | 1 | 0 | 0 | 0 | 0 | |||
(a) | Circuit resistance | 0 | 0 | 0 | |||||
(b) | Luminous efficiency | 3 | 0 | 0 | 1 | 0 | |||
(c) | Molar concentration | 0 | 0 | 0 | 1 | 0 | 0 | ||
(d) | Thermal conductivity | 1 | 1 | 0 | 0 | 0 |
Conclusion:
Thus, the completed table of appropriate dimension for given quantity is shown in Table 1.
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