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[…]
Diodes work as a Rectifier Diode as a Rectifier: The main application of p-n junction diode is in rectification circuits. These circuits are used to describe the conversion of a.c signals to d.c in power supplies. Diode rectifier gives an alternating voltage which pulsates in accordance with time. The filter smoother the pulsation in the Read more about Diodes work as a Rectifier[…]
Maxima and Minima Maximum: Let f (x) be function with domain D ⊂ R then f (x) is said to attain the maximum value at a point a ϵ D if f (x) ≤ f (a) ∀ x ϵ D. The point is called the point maximum f (a) is known as Maximum value of Read more about Maxima and Minima[…]
Special Purpose p – n Junction Diode Zener Diode: ⇒ It is a special purpose diode named after the inventor C. ⇒ It is designed to operate under reverse bias in the breakdown region. ⇒ The symbol for Zener diode is: ⇒ Fabrication – It has heavily doped p – side and n – side. Due to this, Read more about Special Purpose p – n Junction Diode[…]
Geometrical Interpretation of definite Integral If f(x) > 0 for all x ϵ [a, b] then is numerical equal to the area bounded by the curve y = f(x) then x-axis and the straight lines x = a and x = b. = Area LAMB. In general, represented an algebraic sum of the areas of Read more about Geometrical Interpretation of definite Integral[…]
Series and Parallel Capacitors When capacitors are connected in series the total capacitance is less than any one of the series capacitors’ individual capacitance. If two or more capacitors are connected in series the overall effect is that of a single (equivalent) capacitor having the sum total of the plate spacing’s of the individual capacitors. Read more about Series and Parallel Capacitors[…]