qr code vb.net source Fig. 21-A in Visual Studio .NET

Encoder Code 128A in Visual Studio .NET Fig. 21-A

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the manner of Fig. 18-A, approaching the limiting value of zero. Thus, as time increases, the voltage across the capacitor rises, in an exponential-type curve, toward the nal limiting value of V volts. Letting vc denote the voltage across the capacitor, the relationship between vc and time t is shown graphically in Fig. 22-A, the equation of the curve being vc V 1  t=RC 7-A
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Fig. 21-A
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Fig. 22-A
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Note that when t 0, then vc 0, as already mentioned and as shown in Fig. 22-A. Then, as time increases, the term  t=RC decreases exponentially toward the value zero (as in Fig. 18-A). Thus, as t increases, the voltage vc increases toward the limiting value of V volts, as shown in Fig. 22-A. In Fig. 22-A, note that time is expressed in multiples of RC. This can be done because the product ohms times farads is time in seconds, as the following shows. First, by Ohm s law, R in ohms and then by eq. (184), C in farads hence, RC volts seconds coulombs seconds coulombs volts coulombs volts volts volts volts seconds amperes coulombs=sec coulombs
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The product, ohms times farads, is called the time constant of the basic series circuit of Fig. 21-A. As Fig. 22-A shows, at the end of one time constant (RC seconds) the voltage across the capacitor has risen to 63% of its nal value of V volts. (To show this, set t RC in eq. (7-A).)
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Note 15.
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xL is in Ohms
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First, ! 2f 2=T, where T is time of one cycle (eq. (91), Chap. 5). Thus, since  is simply the ratio of two lengths, we see that ! is basically measured in terms of 1=T, that is, in reciprocal seconds.
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Next, by eq. (181) of Chap. 7, L hence, !L 1 volts seconds volts ohms seconds amperes amperes volts volts seconds amperes=seconds amperes
Note 16.
" " j Z Z Rotated through 90 Degrees
" Z A j
Let us make use of the exponential form of a complex number (section 6.5) as follows. " Let Z be a complex number of magnitude A and angle ; thus
then " j Z Aj j But note that  j908 cos 908 j sin 908 j; thus the preceding expression becomes " j Z A j908  j A j  908 " " showing that j Z is equal to Z rotated through 908.
Note 17.
1/xC is in Ohms
From note 15, ! is measured in reciprocal time, 1=T, while capacitance C is measured in coulombs per volt, q=v (eq. (184) in Chap. 7). Thus 1=!C is basically measured in units of 1 volts volts ohms 1 coulombs coulombs=second* amperes second volts
Note 18.
Harmonic Frequencies. Fourier Series
If any particular frequency, f, is taken to be a fundamental frequency, then any INTEGRAL MULTIPLE of f is said to be a harmonic of f. Thus, 2f is the second harmonic of f, 3f is the third harmonic of f, and so on, so that nf is any nth harmonic of f, where n 1; 2; 3; . . . (for n 1 we have fundamental instead of rst harmonic ). Now suppose we have some kind of non-sinusoidal function which occupies the interval from x 0 to x 2, and which is exactly repeated, over and over, endlessly, for all positive and negative intervals of 2, as in Fig. 23-A.
* Coulombs per second is amperes.
Appendix
Fig. 23-A
It is a fact that ANY such repeating function, as met in engineering, can, for purposes of analysis, be considered to be composed of a FUNDAMENTAL sinusoidal wave plus, in general, an in nite number of sinusoidal harmonics of the fundamental wave.* This is a fact of great usefulness because it allows us, by the principle of superposition, to apply the ordinary algebra of complex numbers to the analysis of networks to which non-sinusoidal waves are applied. In such a representation, each complete fundamental wave (which is the lowest frequency component) covers a distance of 2 radians on the x-axis. Hence, in a distance of 2 radians there will be two complete second harmonic waves, three complete third harmonic waves, and so on. Let us discuss, as an interesting example, the symmetrical square wave of Fig. 24-A.
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