Expressions Of Pj Problems

Pj Problems - Overview

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7 Spaces Of Interest - Overview

Triadic Unit Mesh

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COHN - Natures Engineering Of The Human Body

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Differential Calculus

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Painting

Average AC Power And Reactive Power Absorbed By A Load

The AC circuit of figure 1.1 has:

effective voltage = RMS voltage = V_{s} = 320 V,

Internal impedance of V_{s} = Z_{s} = 50 Ω + j100Ω

Load impedance, Z_{L} = 200 Ω + j100Ω

Calculate:
**(a)** The average power and reactive power deliverd by V_{s}.
**(b)** The average power and reactive power absorbed by the load.
**(c)** A reactive element jX is added in parallel to Z_{L}. Find the X such that power delivered to Z_{L} is maximized.

**The strings**:
S_{7}P_{3}A_{32} (force-push).
**The math**:

Pj Problem of Interest is of type *force* (push).

**(a)**Equations: average power P_{avg} = V_{rms}I_{rms}cosθ

Reactive power = Q = V_{rms}I_{rms}sineθ

Z_{eq} = Z_{s} + Z_{L}

So, Z_{eq} = 50 + j100 + 200 + j100 = 250 + j200

So, |Z_{eq}| = [(250)^{2} + (200)^{2}]^{1/2}.

So, |Z_{eq}| = [102500]^{1/2} = 320 Ω.

So, I_{rms} = V_{rms}/Z_{eq} = 320/320 = 1 A.

Cosθ = 250/320 = 0.78125.

So, P_{avg} = V_{rms}I_{rms}cosθ = 320 x 1 x 0.78125 = 250 W.

Sineθ = 200/320 = 0.625

So, reactive power = Q = 320 x 1 x 0.625 = 200 VAR (volt-amperes-reactive).
**(b)** P_{avg absorbed by Load} = P_{avg} - P_{avg dissipated by Zs}.

Z = 50 + j100.

So, |Z_{s}| = [(50)^{2} + (100)^{2})]^{1/2} = [12500]^{1/2} = 111.8.

So, V_{Zs} = I_{Zs}|Z_{s}| = 1 x 111.8 =111.8

So, P_{avg dissipated by Zs} = 111.8 x 1 x (50/111.8) = 50 W

So, P_{avg absorbed by Load} = 250 - 50 = 200 W.

So, Q_{of Zs} = 111.8 x 1 x (100/111.8) = 100 VAR

So, Q_{load} = 200 - 100 = 100 VAR.
**(c)** Maximum power transfer theorem: to transfer maximum power to a load in an AC circuit, the equivalent source impedance and equivalent load impedance must be *matched*, that is, equivalent load impedance must be the conjugate of equivalent source impedance.

So, conjugate of (200 + j100 || jX) = 50 + j100.

X = -100 Ω satisfies the equation.

Math

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 = x^{2} 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

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