Instantaneous Voltages

First, we consider the case that an ac voltage V = Va sin 2nft is applied on both y quadrants, as shown in Fig. 9.13. In this case, only uniform elongation or contraction is present. The frequency / is assumed to be much lower than the resonance frequency of the tube. At each instant, the tube is in equilibrium. In response to the instantaneous voltage V, a strain in the two y quadrants is generated ... 

Thus, if L = 0.05 H and C = 100 pF, the maximum instantaneous voltage developed is 5366 V, which is sufficient to cause a spark to be struck across the switch contacts with consequent damage. 

The capacitor voltage, U can be measured only across the capacitance and the series resistance taken together. At time zero, there is an instantaneous voltage drop due to the current in the series resistance, Rs /TO). The discharging process across a load resistance, R, has then a time constant (Equation 11.9). 

Besides being step-down in principle, linear regulators have another limitation — poor efficiency. Let us understand why that is so. The instantaneous power dissipated in any device is by definition the cross-product V x I, where V is the instantaneous voltage drop across it and I the instantaneous current through it. In the case of the series-pass transistor, under steady application conditions, both V and I are actually constant with respect to... 

If the vector quantity is current or voltage, the instantaneous current i or instantaneous voltage r ai lime t is given b (see Figure 2-6b) ... 

Subsllintioii of this e.xpression into I-aiiiaiioii 2 31 yields, alter rearningemenl. an cxpicssion for the instantaneous voltage across the capacitoi... 

Figure 15.12 Instantaneous voltages and currents in an induction motor supplied from a voltage source inverter.

Figure 15.13 Instantaneous voltages and currents in an indnction motor snpplied from a cnrrent source inverter.

Many of these meters will, at the flip of a switch, show instantaneous voltage or current values or even both in the same display. The price goes up as more features—low-volt-age disconnect, alarms, load shunting, etc.—are added in other models. These aren t bells and whistles. They re the eyes and ears of your system, and will help you make good decisions and spot trouble early. At best, it will make you master of your energy-generating system. At least, it provides a solid sense of security when it comes to energy matters. 

Fig. 5.22 (a) Capacitive circuit, (b) Instantaneous voltage and current, and (c) Vector diagram. 

Figure 5.24a shows a circuit that includes resistance, inductive reactance, and capacitive reactance. The phasor diagram is shown in Fig. 5.24b. The voltage phasor is the-sum of the phasors of the individual voltages. The maximum and instantaneous voltages are presented as capital V and small v, respectively. The instantaneous voltages, V, Vr, Vl, are projections on the horizontal axis in Fig. 5.24b of Fr, Fl, and Fc phasors. The potential difference between the terminals in Fig. 5.24 is in phase with the current in the resistor where the voltage maximum value is Fr = IR.

Transients generated on the antenna side because of a lightning discharge are no less troublesome. The tower is a conductor, and any conductor is also an inductor. A typical 150-ft self-supporting tower may exhibit as much as 40 /xH inductance. During a fast-rise-time lightning strike, an instantaneous voltage drop of 360 kV between the top of the tower and the base is not unlikely. If the coax shield is bonded to... 

Rate of Voltage Change in an RC Circuit To obtain an expression for the instantaneous voltage across the resistor v , we use Ohm s law to substitute i — Vif/R and Vr/R into Equation 2-35 and rearrange to obtain... 

Several important properties of a series RC circuit are illustrated by the results obtained in Example 2-4. First, the sum of the peak voltages for the resistor and the capacitor are not equal to the peak voltage of the source. At the lower frequency, for example, the sum is 21.1 V compared with 20.0 V for the source. This apparent anomaly is understandable when we realize that the peak voltage occurs in the resistor at an earlier time than in the capacitor because of the voltage lag in the latter. At any time, however, the sum of the instantaneous voltages across the two elements equals the instantaneous voltage of the source. 

The Thevenin equivalent circuit is the simplest combination, since it is the association of an ideal voltage source and a resistor connected in series. This is a much more realistic way of modeling a lead-acid battery. Indeed, the resistor illustrates the voltage drop due to the current passing through the components of the battery. In the case of LABs, this instantaneous voltage drop mainly results from the low electrical conductivity of electrolyte and is proportional to the current. But, such a simple combination does not account for the polarization of the electrodes happening later on, when the battery is operated. 

A Marx impulse generator had typical pulse risetimes of order 20 ys with decay times of order 6 ms. At early times the electric field is uniform, given by V/d where V is the Instantaneous voltage across electrodes of spacing d. The transmitted light distribution in the interelectrode region is then also uniform as shown in Fig. 13 for X =... 

Fig. 30. For no space charge, the electric field distribution Is uniform at V/1, where V Is the Instantaneous voltage and 1 = 1 cm is the electrode spacing, so that the Kerr effect shows uniform light transmission in the interelectrode gap region for all electrode combinations in highly purified water. E os35-36 kV/cm. In each photograph of...

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