Tag: Free Book on AC
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4.5 Capacitor Quirks
As with inductors, the ideal capacitor is a purely reactive device, containing absolutely zero resistive (power dissipative) effects. In the real world, of course, nothing is so perfect. However, capacitors have the virtue of generally being purer reactive components than inductors. It is a lot easier to design and construct a capacitor with low internal…
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4.4 Parallel Resistor-Capacitor Circuits
Using the same value components in our series example circuit, we will connect them in parallel and see what happens: Parallel R-C circuit. Resistor and Capacitor in Parallel Because the power source has the same frequency as the series example circuit, and the resistor and capacitor both have the same values of resistance and capacitance,…
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4.3 Series Resistor-Capacitor Circuits
In the last section, we learned what would happen in simple resistor-only and capacitor-only AC circuits. Now we will combine the two components together in series form and investigate the effects. Series capacitor circuit: voltage lags current by 0° to 90°. Impedance Calculation The resistor will offer 5 Ω of resistance to AC current regardless…
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4.2 AC Capacitor Circuits
Capacitors Vs. Resistors Capacitors do not behave the same as resistors. Whereas resistors allow a flow of electrons through them directly proportional to the voltage drop, capacitors oppose changes in voltage by drawing or supplying current as they charge or discharge to the new voltage level. The flow of electrons “through” a capacitor is directly…
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4.1 AC Resistor Circuits (Capacitive)
Pure resistive AC circuit: voltage and current are in phase. If we were to plot the current and voltage for a very simple AC circuit consisting of a source and a resistor, (figure above) it would look something like this: (figure below) Voltage and current “in phase” for resistive circuit. Because the resistor allows an…
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3.6 What Is the Skin Effect?
The Skin Depth of Copper in Electrical Engineering As previously mentioned, the skin effect is where alternating current tends to avoid travel through the center of a solid conductor, limiting itself to conduction near the surface. This effectively limits the cross-sectional conductor area available to carry alternating electron flow, increasing the resistance of that conductor…
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3.5 Inductor Quirks
In an ideal case, an inductor acts as a purely reactive device. That is, its opposition to AC current is strictly based on inductive reaction to changes in current, and not electron friction as is the case with resistive components. However, inductors are not quite so pure in their reactive behavior. To begin with, they’re…
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3.4 Parallel Resistor-Inductor Circuits
Let’s take the same components for our series example circuit and connect them in parallel: Parallel R-L circuit. Because the power source has the same frequency as the series example circuit, and the resistor and inductor both have the same values of resistance and inductance, respectively, they must also have the same values of impedance.…
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3.3 Series Resistor-Inductor Circuits
In the previous section, we explored what would happen in simple resistor-only and inductor-only AC circuits. Now we will mix the two components together in series form and investigate the effects. Series Resistor Inductor Circuit Example Take this circuit as an example to work with: Series resistor inductor circuit: Current lags applied voltage by 0o…
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3.2 AC Inductor Circuits
Resistors vs. Inductors Inductors do not behave the same way as resistors do. Whereas resistors simply oppose the flow of current through them (by dropping a voltage directly proportional to the current), inductors oppose changes in current through them, by dropping a voltage directly proportional to the rate of change of current. In accordance with…
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3.1 AC Resistor Circuits (Inductive)
Pure resistive AC circuit: resistor voltage and current are in phase. If we were to plot the current and voltage for a very simple AC circuit consisting of a source and a resistor (figure above), it would look something like this: (figure below) Voltage and current “in phase” for resistive circuit. Because the resistor simply…
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2.8 Some Examples with AC Circuits
Let’s connect three AC voltage sources in series and use complex numbers to determine additive voltages. All the rules and laws learned in the study of DC circuits apply to AC circuits as well (Ohm’s Law, Kirchhoff’s Laws, network analysis methods), with the exception of power calculations (Joule’s Law). The only qualification is that all…
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2.7 More on AC polarity
Complex numbers are useful for AC circuit analysis because they provide a convenient method of symbolically denoting phase shift between AC quantities like voltage and current. However, for most people, the equivalence between abstract vectors and real circuit quantities is not an easy one to grasp. Earlier in this chapter, we saw how AC voltage…
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2.6 Complex Number Arithmetic
Since complex numbers are legitimate mathematical entities, just like scalar numbers, they can be added, subtracted, multiplied, divided, squared, inverted, and such, just like any other kind of number. Some scientific calculators are programmed to directly perform these operations on two or more complex numbers, but these operations can also be done “by hand.” This…
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2.5 Polar Form and Rectangular Form Notation for Complex Numbers
In order to work with complex numbers without drawing vectors, we first need some kind of standard mathematical notation. There are two basic forms of complex number notation: polar and rectangular. Polar Form of a Complex Number The polar form is where a complex number is denoted by the length (otherwise known as the magnitude,…