Expressions Of Pj Problems
Average AC Power

Average AC Power
Figure 8.7 shows a simple AC circuit. Figure 8.7(a) is the time domain circuit while figure 8.7(b) is its phasor form.
Given that the sinusoidal voltage and current of the circuit are as follows:
v(t) = Vcos(ωt); i(t) = Icos(ωt - θ); Determine:
(a) The average power of the circuit in the time domain
(b) The average power of the circuit in the frequency domain.

The string:
S7P3A32 (Force - Push).
The math:
Average AC Power
Pj Problem of interest is of type force. Power and energy problems are force problems. Electric power is a force-push.

(a) General expression for electric power is:
p(t) = v(t)i(t)
So, p(t) = VIcos(ωt)cos(ωt - θ)----(1)
Using the following identities of trigonometry:
2cos2ωt - 1 = cos2(ωt) and cosωtsinωt = (sin2ωt)/2 .
Equation (1) reduces to:
p(t) = (VI/2)cos(θ) + (VI/2)cos(2ωt - θ) ----(2)
(a) The average power, Pav is obtained by integrating p(t) over one cycle of the sinusoidal signal and dividing by the period T, of the signal.
Average AC Power
So, after substituting the expression for p(t) in equation (2) and integrating, we have:
Pav = (VI/2)cosθ

(b) In the frequency domain:
V(jω) = Vej0 and I(jω) = Ie-jθ
So, impedance, Z = (V/I)e
So, I = (V/|Z|)e
Hence, Pav = (V2/2)(1/|Z|)cosθ = (I2/2)(|Z|)cosθ
rms values are usually used for the voltage and current amplitudes.
Where, Vrms = V/√2 and Irms = I/√2.


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
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

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

What is Time?
St Augustine On Time
Bergson On Time
Heidegger On Time
Kant On Time
Sagay On Time
What is Space?
Newton On Space
Space Governance
Imperfect Leaders
Essence Of Mathematics
Toolness Of Mathematics
The Number Line
The Windflower Saga
Who Am I?
Primordial Equilibrium
Primordial Care
Force Of Being

Blessed are they that have not seen, and yet have believed. John 20:29

TECTechnic Logo, Kimberlee J. Benart | © 2000-2021 | All rights reserved | Founder and Site Programmer, Peter O. Sagay.