Torque on an Electric Dipole in a Uniform Electric Field Consider a dipole with charges +q and –q forming a dipole since they are a distance d away from each other. Let it be placed in a uniform electric field of strength E such that the axis of the dipole forms an angle θ with Read more about Torque on an Electric Dipole in a Uniform Electric Field[…]
Fundamental Forces in Nature What are the Fundamental Forces in Nature? There are four universal or fundamental forces in nature. Without these forces, all matter in the world will fall apart. Force as such is any pull or push that causes an object to alter its physical state (in terms of motion or deformity). Newton Read more about Fundamental Forces in Nature[…]
Differential Equations An equation involving one dependent variable, one or more independent variable and the differential coefficient (derivatives) of dependent variable with respect to independent variable is called differential equations. Examples: 1. , 2. . Types of differential equations 1. Ordinanry differential equation: A differential equations is said to be an ordinary differential equation. If Read more about Differential Equations[…]
Indefinite Integration – Direct Subtitution Definition: If f(x) and g(x) are two functions such that f'(x) = g(x) then f(x) is called antiderivative or primitive of g(x) with respect to x Note1: If f(x) is an antiderivative of g(x) then f(x)+c is also an antiderivative of g(x) for all c ϵ wR If F(x) is an Read more about Indefinite Integration – Direct Subtitution[…]
Electrical Resistance What is Electrical Resistance? According to Ohm’s law, there is a relation between the current flowing through a conductor and the potential difference across it. It is given by, V ∝ I V = IR Where, V = potential difference measured across the conductor (in volts). I = Current through the conductor (in amperes). Read more about Electrical Resistance[…]
Newton-Leibnitz Formula, Integral Function and its Properties Let f(x) be a continuous function defined on [a, b], then a function ф(x) defined by for all x ϵ [a, b] Is called the integral function of the function f(x)x Property I: The integral function of an integrable function is always continuous. Property II: If ф(x) is differentiable Read more about Newton-Leibnitz Formula, Integral Function and its Properties[…]
Temperature dependence of Resistance Resistance is fundamentally the ability of the material to restrict the passage of electric current. Thus, just as material properties such as density, size, magnetization etc. change with temperature, so doe’s resistance. Resistance is really a bulk property; the resistivity on the other hand is a material property. Resistivity of Metals: The resistivity Read more about Temperature dependence of Resistance[…]
Voltage and Current Dividers Voltage Divider: A voltage divider is a simple circuit which turns a large voltage into a smaller one. Using just two series resistors and an input voltage, we can create an output voltage that is a fraction of the input. Voltage dividers are one of the most fundamental circuits in electronics. It is interesting and useful to consider Read more about Voltage and Current Dividers[…]
MAXIMA AND MINIMA PROBLEMS 1. Without using the derivative, show that f(x) = (½)x is strictly decreasing on R. Solution: Given that f(x) = (½)x Let x₁, x₂ ϵ R Let x₁ < x₂ ⇒ (½)x₁ > (½)x₂ ⇒ f(x₁) > f(x₂). ∴ f is strictly decreasing on R. 2. Without using the derivative, show Read more about MAXIMA AND MINIMA PROBLEMS[…]
Global Maxima or Minima Global Maxima or Minima in [a, b]: Global maxima or minima of f(x) in [a, b] is basically the greatest or least value of f(x) in [a, b]. Mathematically, it is written as: The function f(x) has a global maximum at the point ‘a’ in the interval I if f (a) ≥ Read more about Global Maxima or Minima[…]