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AC by Tony R. Kuphaldt PDF

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By Tony R. Kuphaldt

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However, when we begin to analyze alternating current circuits, we find that quantities of voltage, current, and even resistance (called impedance in AC) are not the familiar one-dimensional quantities we’re used to measuring in DC circuits. Rather, these quantities, because they’re dynamic (alternating in direction and amplitude), possess other dimensions that must be taken into account. Frequency and phase shift are two of these dimensions that come into play. Even with relatively simple AC circuits, where we’re only dealing with a single frequency, we still have the dimension of phase shift to contend with in addition to the amplitude.

3 Simple vector addition Remember that vectors are mathematical objects just like numbers on a number line: they can be added, subtracted, multiplied, and divided. Addition is perhaps the easiest vector operation to visualize, so we’ll begin with that. If vectors with common angles are added, their magnitudes (lengths) add up just like regular scalar quantities: length = 6 angle = 0 degrees length = 8 total length = 6 + 8 = 14 angle = 0 degrees angle = 0 degrees Similarly, if AC voltage sources with the same phase angle are connected together in series, their voltages add just as you might expect with DC batteries: 6V 0 deg + - 8V 0 deg + 14 V 0 deg - 6V + - + - 14 V 8V + + Please note the (+) and (-) polarity marks next to the leads of the two AC sources.

COMPLEX NUMBERS 22 ∠ -64o 15 ∠ 0o 12 ∠ 35o The sum of these vectors will be a resultant vector originating at the starting point for the 22 volt vector (dot at upper-left of diagram) and terminating at the ending point for the 15 volt vector (arrow tip at the middle-right of the diagram): resultant vector 22 ∠ -64o 15 ∠ 0o 12 ∠ 35o In order to determine what the resultant vector’s magnitude and angle are without resorting to graphic images, we can convert each one of these polar-form complex numbers into rectangular form and add.

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AC by Tony R. Kuphaldt


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