Dimensions of Fundamental Quantities
Unit, Dimensions, and measurements > Dimensions
Dimensions
- The power to which fundamental quantities must be raised in order to express the given physical quantity are called its dimensions.
- To make it more clear, consider the physical quantity force
Force = mass X acceleration
= mass x velocity/time
= mass x (length/time)/time
= mass x length x (time)2 …(i)
Thus the dimensions of force are 1 in mass, 1 in length and -2 in time.
Thus equation (i) can be written as [force] = [MLT-2]
Important dimensions of complete physics
Heat
| Quantity | Unit | Dimension |
|---|---|---|
| Temperature(T) | Kelvin | [M0L0T0θ1] |
| Heat(Q) | Joule | [ML2T-2] |
| Specific heat(c) | Joule/kg-K | [M2L2T-2θ-1] |
| Thermal capacity | Joule/K | [M1L2T-2θ-1] |
| Latent heat(L) | Joule/kg | [M0L2T-2] |
| Gas Constant(R) | Joule/mol-K | [ML2T-2θ-1mol-1] |
| Boltzmann Constant (K) | Joule/K | [M1L2T-2θ-1] |
| Planck’s constant(h) | Joule-s | [M1L2T-1] |
Electricity
| Quantity | Unit | Dimension |
|---|---|---|
| Electric charge(q) | Coulomb | [M0L0T1A1] |
| Electric current(I) | Ampere | [M0L0T0A1] |
| Electric potential(V) | Joule/coulomb | [M1L2T-3A-1] |
| Dielectric constant(K) | Unitless | [M0L0T0] |
Significant figures
Significant figures in the measured value of a physical quantity tell the number of digits in which we have confidence. Larger the number of significant figures obtained in a measurement, greater is the accuracy of the measurement. The reverse is also true.
- All non-zero digits are significant.
Example: 64.7 has three significant figures. - A zero becomes a significant figure if it appears between two non-zero digits.
Example: 2.98 has three significant figures. - Leading zeros or the zeros placed to the left to the number are never significant.
Example: 0.879 has three significant figures. - Trailing zeroes or the zeroes placed to the right of the number are
significant.
Example: 2.270 has four significant figures. - In exponential notation, the numerical portion gives the number of
significant figures. Example: 2.24 x 10-3 has three significant figures.
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