*What is a scalar?
*What is a scalar? If a physical quantity can be completely described by telling its magnitude only and direction is meaningless for it, then it is called a scalar.
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^Type of physical quantities
^Type of physical quantities Physical quantities can be categorized in following four types: (a) Scalars (b) Vectors (c) Ratios (d) Tensors
^Limitations of dimensions
^Limitations of dimensions Dimensional analysis does not give any information about the scalar or vector nature of the quantity. Dimensions for v = u + at etc. can’t be calculated in exact form. Dimensional formulae of the quantities depending on more than three variables cannot be obtained. Dimensional formulae of the quantities involving trigonometric logarithmic […]
^Uses of dimensions
^Uses of dimensions Correctness of a physical relation can be checked dimensionally. If dimensions of both the sides are found to be same, then the relation is said to be correct otherwise incorrect. Dimension of unknowns can be calculated. A mathematical relation between two or three quantities (called a physical relation) can be derived. Two […]
^Parallel plate capacitor
Parallel plate capacitor If the plates X & Y have equal & opposite charges, then charge distribution on plates is as shown in the adjacent drawing. Usually for a parallel plate capacitor we consider this picture. Let A is the area of each plate, then the charge density of face A, b, c & d […]
*A quantity having dimensions must posses some units, where as dimensionless quantity can have units. e.g. angle.
Facts *A quantity having dimensions must posses some units, where as dimensionless quantity can have units. e.g. angle. Relative velocity have same dimensions as that of velocity where as relative density is dimensionless.
^Dimensionless Quantities
^Dimensionless Quantities Strain, angle, solid angle, all Trigonometric ratios, all real numbers, logarithmic functions, exponential functions, Poisson’s ratio, refractive index, relative density, relative permittivity, relative permeability, fine structure constant etc. have no dimensions.
*Dimensional Variables
*Dimensional Variables Are the physical quantities which have dimensions as well as variable values. e.g. Force, Mass, Velocity, Area, Volume etc.
^Dimensionless Variables
^Dimensionless Variables Are the physical quantities which have no dimensions but have variable values. e.g. Angle, Strain, Specific gravity etc.
*Dimensional Constants
*Dimensional Constants All constants are not dimensionless. The physical quantities which have constant values and dimensions as well are called dimensional constants. e.g. Planck’s constant, Boltzmann’s constant & Gravitational constant etc.
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