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5. POLAR AND RECTANGULAR NOTATION 35 with a lower-case ”i” (in pure mathematics) or ”j” (in electronics). These lower-case letters do not represent a physical variable (such as instantaneous current, also symbolized by a lower-case letter ”i”), but rather are mathematical operators used to distinguish the vector’s vertical component from its horizontal component. As a complete complex number, the horizontal and vertical quantities are written as a sum: In "rectangular" form, a vector’s length and direction are denoted in terms of its horizontal and vertical span, the first number representing the horixontal ("real") and the second number (with the "j" prefix) representing the vertical ("imaginary") dimensions.

It means that the inductor is releasing power back to the circuit, while a positive power means that it is absorbing power from the circuit. Since the positive and negative power cycles are equal in magnitude and duration over time, the inductor releases just as much power back to the circuit as it absorbs over the span of a complete cycle. What this means in a practical sense is that the reactance of an inductor dissipates a net energy of zero, quite unlike the resistance of a resistor, which dissipates energy in the form of heat.

1 AC resistor circuits R If we were to plot the current and voltage for a very simple AC circuit consisting of a source and a resistor, it would look something like this: e= i= + Time Because the resistor simply and directly resists the flow of electrons at all periods of time, the waveform for the voltage drop across the resistor is exactly in phase with the waveform for the current through it. We can look at any point in time along the horizontal axis of the plot and compare those values of current and voltage with each other (any ”snapshot” look at the values of a wave are referred to as instantaneous values, meaning the values at that instant in time).

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A guide to online information about Peltier thermoelectric coolers by Paddock B.


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