Statistics of polarization speckle produced by a constant polarization phasor plus a random polarization phasor sum

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Phasor Arithmetics01:13

Phasor Arithmetics

Phasors and their corresponding sinusoids are interrelated, offering unique insights into the behavior of alternating current (AC) circuits. One way to understand this relationship is through the operations of differentiation and integration in both the time and phasor domains.
When the derivative of a sinusoid is taken in the time domain, it transforms into its corresponding phasor multiplied by j-omega (jω) in the phasor domain, where j is the imaginary unit, and ω is the angular...
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Potential Due to a Polarized Object01:29

Potential Due to a Polarized Object

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
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Phasors01:12

Phasors

Phasors are a powerful mathematical tool used to analyze alternating current (AC) circuits. They provide a complex number representation of sinusoids, with the magnitude of the phasor equating to the amplitude of the sinusoid and the angle of the phasor representing the phase measured from the positive x-axis.
One of the significant benefits of using phasors is that they simplify the analysis of AC circuits by eliminating the time dependence of the current and voltage. This transformation...
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Phasor Relationships for Circuit Elements01:16

Phasor Relationships for Circuit Elements

Phasor representation is a powerful tool used to transform the voltage-current relationship for resistors, inductors, and capacitors from the time domain to the frequency domain. This transformation simplifies the analysis of alternating current (AC) circuits.
In the time domain, Ohm's law provides a fundamental relation between the current flowing through a resistor and the voltage across it:
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Susceptibility, Permittivity and Dielectric Constant01:26

Susceptibility, Permittivity and Dielectric Constant

When placed in an external electric field, a dielectric material gets polarized. The charge density in the dielectric material is given by the sum of the bound and free charge densities, while the total charge density can also be written in terms of the total electric field. The bound charge density can be measured in terms of polarization, leading to the relationship between electric displacement and polarization.
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Kirchoff's Laws using Phasors01:12

Kirchoff's Laws using Phasors

Analyzing AC circuits in electrical systems is a fundamental aspect of electrical engineering. In these circuits, AC power is supplied from a distribution panel and wired to various household appliances in parallel. To perform a comprehensive analysis, electrical engineers use Kirchhoff's voltage and current laws, which are equally applicable in AC circuits as in DC circuits.
Kirchhoff's voltage law (KVL) states that the sum of phasor voltages around a closed loop in an AC circuit equals zero....
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