Complete the following table.
Dimensions | ||||||||||
Quantity | SI Units | M | L | T | Θ | N | J | I | ||
Example | Acoustic impedance | (Pa s)/m | 1 | –2 | –1 | 0 | 0 | 0 | 0 | |
(a) | Circuit resistance | V/A | ||||||||
(b) | Luminous efficacy | cd/W | ||||||||
(c) | Thermal conductivity | cal/(cm s oC) |
Fill the appropriate dimensions for given quantity and complete the table.
Answer to Problem 1ICA
The completed table of appropriate dimension for given quantity is shown in Table 1.
Explanation of Solution
Given data:
The SI unit of circuit resistance is
The SI unit of luminous efficacy is
The SI unit of thermal conductivity is
Calculation:
Refer to Table 9-1 in the textbook for fundamental dimensions and base unit.
Refer to 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
Find the fundamental dimension of resistance.
Substitute
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 (cd) is J.
Find the fundamental dimension of power.
Refer to Table 8-14 in the textbook for summary of electrical properties.
Substitute
Substitute J for cd and
Calories can be measured in terms of Joules.
Find the fundamental dimension of thermal conductivity.
Refer to Table 8-11 in the textbook for dimension of energy, to represent the dimensions of required parameters.
Substitute J for cal in equation (2) 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 | 1 | 2 | 0 | 0 | 0 | |||
(b) | Luminous efficiency | 0 | 0 | 0 | 1 | 0 | 0 | ||
(c) | 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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