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The Phosphorus Cycle01:21

The Phosphorus Cycle

Unlike carbon, water, and nitrogen, phosphorus is not present in the atmosphere as a gas. Instead, most phosphorus in the ecosystem exists as compounds, such as phosphate ions (PO43-), found in soil, water, sediment and rocks. Phosphorus is often a limiting nutrient (i.e., in short supply). Consequently, phosphorus is added to most agricultural fertilizers, which can cause environmental problems related to runoff in aquatic ecosystems.
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Phosphorylation01:02

Phosphorylation

The addition or removal of phosphate groups from proteins is the most common chemical modification that regulates cellular processes. These modifications can affect the structure, activity, stability, and localization of proteins within cells as well as their interactions with other proteins.
During phosphorylation, protein kinases transfer the terminal phosphate group of ATP to specific amino acid side chains of substrate proteins. Serine, threonine, and tyrosine are the most commonly...
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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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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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