Dielectric constant
Dielectric constant is also called relative permittivity or specific inductive capacity & is defined as
K = 1 (air or vacuum), K = 81 (water),
K = ∞ (metals), K = 0 (insulator)
Dielectric constant decreases on heating.
*Graph of logarithmic function
The function y = logb x is called a logarithmic function, it is not defined for x ≤ 0.
It is a decreasing function for 0 < b & increasing for b > 1. The y – axis is an asymptote of the curve
y = logb x. The x intercept is the point (1, 0).
*Up or down parabola
A quadratic of the form y = ax2 + bx + c represents an upward or a downward parabola, it can also be expressed by the following function
(x – u)2 = L (y – v)
L= +ve for upward parabola & L = – ve for a downward parabola.
*Shape of y versus x graph
Let a physical quantity y depends on other physical quantity x, this dependence is called a mathematical function & usually expressed as
y = f (x) (read as y is a function of x).
The dependence of y on x can be visualised by drawing a graph of function y = f (x). While plotting graphs the independent varaible is taken on horizontal line & dependent on vertical line. Shape of y versus x graph depends on the type of function.
Following types of y versus x graphs are frequently encountered in Physics.
*Laws of log
*Componendo & dividendo
*Bounded functions
If a function attains finite values only, then it is said to be bounded otherwise unbounded.
Only sinθ & cosθ are bounded functions, secθ, cosθ, tanθ & cotθ are unbounded.
*Transformation formulae
sinA + sinB = 2sinC cosD
sinA – sinB = 2cosC sinD
cosA + cosB = 2cosC cosD
cosA – cosB = – 2sinC sinD
*Quadrant system Signs of T – ratios are actually sign of cartesian coordinate system.
^A long horizontal fixed wire carries a current of 100 A. Directly above and parallel to it is another wire carrying a current of 20 A and weighing 0.04 N/m. The separation between the two wires so that the upper wire is just supported by the magnetic repulsion is
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