Pj Problems - Overview
Celestial Stars
The Number Line
Geometries
7 Spaces Of Interest - Overview
Triadic Unit Mesh
Creation
The Atom
Survival
Energy
Light
Heat
Sound
Music
Language
Stories
Work
States Of Matter
Buoyancy
Nuclear Reactions
Molecular Shapes
Electron Configurations
Chemical Bonds
Energy Conversion
Chemical Reactions
Electromagnetism
Continuity
Growth
Human-cells
Proteins
Nucleic Acids
COHN - Natures Engineering Of The Human Body
The Human-Body Systems
Vision
Walking
Behaviors
Sensors Sensings
Beauty
Faith, Love, Charity
Photosynthesis
Weather
Systems
Algorithms
Tools
Networks
Search
Differential Calculus
Antiderivative
Integral Calculus
Economies
Inflation
Markets
Money Supply
Painting
The differential op-amp can be presented in more than one way. Figure 12.1 illustrates one of the ways.
Find the output voltage Vo of figure 12,1 and indicate the mathematical operation performed by the op-amp circuit. Assume the op-amp is an ideal op-amp.
The strings:
S7P5A51 (change - physical).
The math:
Pj Problem of Interest is of type change (physical - change).
Consider figure 12.1. If the op-amp is an ideal op-amp then V - V2 = Vd = 0 approximately, V = V2, AOL is infinitely large, and current into op-amp, iin = 0.
Figure 12.1 can be viewed as a combination of a noniverting op-amp and an inverting op-amp.
Consider the ideal noninverting op-amp (first op-amp in figure 12.1):
output voltage = Vo1 = ( 1 + R1/R2)V1
So, V = (1 + R1/R2)V1 - i1R1
But V = V2
So, (1 + R1/R2)V1 - i1R1 = V2--------(1)
Consider the inverting op-amp (second op-amp i figure 12.1):
Current i1, through R1 of the inverting op-amp = current through R2 of the inverting op-amp
So, i1 = (V - Vo)/R2
So, i1 = [(1 + R1/R2)V1 - i1R1 - Vo]/R2
So, i1 = V1/R2 - Vo/(R1 + R2)------- (2)
So, substituting the value of i1 of eq(2) into eq (1), we have:
(R2 + R1)/R2)V1 - [V1/R2 - Vo/(R1 + R2)]R1 = V2
So, V1[((R2 + R1)/R2) - (R1/R2)] - (R1Vo)/(R1 + R2) = V2
So, V1 + (R1Vo)/(R1 + R2) = V2
So, Vo = (1 + R2/R1)(V2 - V1).
So, op-amp is a subtractor.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring
Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle
Derivation Of The Area Of An Ellipse
Derivation Of Volume Of A Cylinder
Derivation Of Volume Of A Sphere
Derivation Of Volume Of A Cone
Derivation Of Volume Of A Torus
Derivation Of Volume Of A Paraboloid
Volume Obtained By Revolving The Curve y = x2 About The X Axis
Single Variable Functions
Absolute Value Functions
Conics
Real Numbers
Vector Spaces
Equation Of The Ascent Path Of An Airplane
Calculating Capacity Of A Video Adapter Board Memory
Probability Density Functions
Boolean Algebra - Logic Functions
Ordinary Differential Equations (ODEs)
Infinite Sequences And Series
Introduction To Group Theory
Advanced Calculus - Partial Derivatives
Advanced Calculus - General Charateristics Of Partial Differential Equations
Advanced Calculus - Jacobians
Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables
Advanced Calculus - Fourier Series
Advanced Calculus - Multiple Integrals
Production Schedule That Maximizes Profit Given Constraint Equation
Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation
Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions
Fourier Series
Derivation Of Heat Equation For A One-Dimensional Heat Flow
Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition
The Universe is composed of matter and radiant energy. Matter is any kind of mass-energy that moves with velocities less than the velocity of light. Radiant energy is any kind of mass-energy that moves with the velocity of light.
Periodic Table
Composition And Structure Of Matter
How Matter Gets Composed
How Matter Gets Composed (2)
Molecular Structure Of Matter
Molecular Shapes: Bond Length, Bond Angle
Molecular Shapes: Valence Shell Electron Pair Repulsion
Molecular Shapes: Orbital Hybridization
Molecular Shapes: Sigma Bonds Pi Bonds
Molecular Shapes: Non ABn Molecules
Molecular Orbital Theory
More Pj Problem Strings