qr code generator vb.net Fig. 151. i and v IN PHASE. in VS .NET Encoding ANSI/AIM Code 128 in VS .NET Fig. 151. i and v IN PHASE.

Fig. 151. i and v IN PHASE.
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Fig. 152. i and v 908 OUT OF PHASE.
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In the gures v instantaneous voltage, i instantaneous current, thus p vi instantaneous power. FIRST consider Fig. 151. Here v is the voltage applied to a pure resistance of R ohms. From the gure, note that the direction of the current is always the same as the direction of the voltage. Thus, in Fig. 151 we have that from 08 to 1808, p v i p, that is, positive power, from 1808 to 3608, p v i p, that is, positive power. Thus, in this case the generator at all times delivers power to the resistance R. By eq. (227), the power is equal to P VI cos 08 VI watts. Next consider Fig. 152. Here v is a sinusoidal generator voltage applied to a pure capacitance. Note that the direction of the current is not always the same as the direction of the voltage; thus, in Fig. 152 we have that from from from from 08 to 908, p v i p, that is, positive power, 908 to 1808, p v i p, that is, negative power, 1808 to 2708, p v i p, that is, positive power, 2708 to 3608, p v i p, that is, negative power.
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Thus, in this theoretically ideal case (zero resistance), the net power output of the generator is zero; half the time the generator is storing energy in the capacitor, while during the other half the capacitor discharges, tending to run the generator as a motor. Now consider a non-ideal case, having both resistance and reactance, such as the series RC circuit shown in Fig. 153 where, let s assume, the current leads the voltage by, say, 458, as shown in Fig. 154.
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CHAPTER 8 Reactance and Impedance
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Fig. 153
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Fig. 154
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Since we re dealing with alternating current, the generator voltage arrow in Fig. 153 alternately points up and down as the generator alternates in polarity, the arrow always pointing from the negative terminal of the generator to its positive terminal. Positive power is produced by the generator when the current ows through the generator in the direction of the generator voltage arrow. Negative power is produced when current ows through the generator against the generator voltage arrow, thus momentarily running the generator as a motor. This is similar to working with a storage battery; the battery produces power when current ows out of the positive terminal of the battery, but the battery absorbs energy (becomes the load) when current ows into the positive terminal (while the battery is being recharged). For the situation in Fig. 154, note that most of the time the current ows through the generator in the same sense as the generator voltage, so that in this case  458) positive power exceeds negative power. Thus, in this particular case, the true or positive power output of the generator is, by eq. (227), equal to P VI cos 458 0:7071 VI The above discussion of the capacitive circuit of Fig. 153 also applies, of course, to inductive-type loads. In the inductive case energy is stored in the magnetic eld of the inductor coil, the magnetic eld of the coil alternately being charged and discharged ; the inductive action causes the current to lag the applied voltage instead of leading as in the capacitive case illustrated in Fig. 154. Another point to mention is as follows. Inspection of Figs. 151, 152, and 154 shows that instantaneous POWER in an ac circuit always pulsates sinusoidally at a frequency equal to twice the frequency of the applied voltage. This is an important factor that must be taken into account in certain practical design problems. Another point of importance concerns the quantity cos , which we ve called the circuit power factor (see eq. (227)). The power factor, cos , can also be expressed in terms of impedance and power, as follows. In direct-current (dc) work, power, P, is given by the simple relationship P VI. In the ac case, however, average power is given by eq. (227), which let us rewrite as eq. (228), thus P VI cos  228
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where  is the phase angle between the current and voltage waves, and V and I are magnitudes of rms values of voltage and current. Thus, in the ac case, the product VI may or may not be equal to the true power P. For this reason it s appropriate to call the
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