Section 2 Series Circuit

We will see in Section 9.2.3 that, when measuring on a parallel circuit with controlled voltage, the real part of the resulting current will he proportional to the conductance and the imaginary part will he proportional to the susceptance. And furthermore, that if the physical reality is a series circuit, this simple proportionality will he absent, and the values must be mathematically calculated in each case. The same proportionality is also present for controlled current measurements on a series circuit. Values for conductance and susceptance of the skin are thus always related to an opinion on whether these phenomena electrically exist in series or parallel. 

When the resonant LC section is imbedded within the circuit shown in Fig. 1.12, and the source frequency is the same as the resonant frequency of the section, the circuit looks Hke the voltage source is connected to a series circuit consisting of Ri in series with Rq- All of the current from the source is delivered to the output resistor. At other frequencies, the impedance of the LC section provides a path for current to bypass Rq. From this we can conclude, without formal proof, that the circuit implements a bandpass Bode magnitude characteristic like that in Fig. 1.7, but with its peak value scaled by voltage division tohe Ro/ Ri + Rq). 

Figure 4.25 illustrates a numerical model of the single section of the feeding circuit. The substation is expressed by a series circuit of a diode D, an internal resistor R, and a voltage... 

Such relays are normally instantaneous, highly sensitive and operate at low spill cuiTents. Since they detect the residual current of the system, the current may contain third-harmonic components (Section 23.6) and operate the highly sensitive relay in a healthy condition. To avoid operation of the relay under such conditions, it is a normal practice to supply the relay coil with a tuned filter, i.e. a series L-C circuit to filter out the third-harmonic components. The capacitance of the filter circuit may also tame a steep rising TRV (Section 17.10.3) during a momentary transient condition and protect the relay. 

The use of a reactor in series with the ctipacitors w ill reduce the harmonic effects in a power network, as well as their effect on other circuits in the vicinity, such as a telecommunication network (see also Section 23.1 1 and Example 23.4). The choice of reactance should be such that it W ill provide the required detuning by resonating below the required harmonic, to provide a least impedance path for that harmonic and filter it out from the circuit. The basic idea of a filter circuit is to make it respond to the current of one frequency and reject all other frequency components. At power frequency, the circuit should act as a capacitive load and improve the p.f. of the system. For the fifth harmonic, for instance, it should resonate below X 50 Hz for a 50 Hz system, say at around 200-220 Hz, to avoid excessive charging voltages w hich may lead to... 

When a capacitor circuit is compensated through a series reaetor. either to suppress the system harmonics or to limit the switching inrush currents (Section 23.11) or both, it will require suitable adjustment in its voltage and capacitive ratings, fhe series reactor will dampen the switching currents but consume an inductively reactive power and offset an equivalent amount of capacitive kVAr. and require compensation. The following example w ill elucidate this. 

Since the line impedance, R + J (Xl - Xc), will reduce with a series compensation, the fault level of the system will rise. It should not matter if the fault level of the system is determined by the impedance of the source of supply, ignoring any other impedance of the circuit (Section 13.4.1 (5)). Moreover, such a situation is automatically averted through the protection of the series capacitors, as discussed below, by which the capacitors are bypassed during a line fault, the line restoring its original impedance, hence the original fault level. Nevertheless, when it is required to limit the system fault level, inductive coupling circuits may be provided to reduce the fault to the desired level. This is also discussed below ... 

We first consider how the simple analysis of Section 7.3, for the combined doubly cyclic series plant, is modified for the open circuit/closed cycle plant. The work output from the gas-turbine plant of Fig. 7.3 is... 

Refer to tlie time and failure transistor example provided in Section 20.4. Determine tlie 10,000-hour reliability of a circuit of five such transistors connected in series. 

Haupt-satz, m. fundamental principle or law main theorem axiom, -schalter, m. main (or master) switch, -schlagader, /. main artery aorta, -schluss, m. (Elec.) main circuit. -schliissel, m. master key. -schnitt, m. principal section, -schwlngung, /. principal vibration, -serie, /. principal series, -tlcherung,/. (Elec.) main fuse, main cutout. 

Alternately, for potential-step experiments (e.g., chronoamperometry, see Section 3-1), the charging current is die same as that obtained when a potential step is applied to a series RC circuit ... 

An important corollary of the principle of superposition is that a wave of any shape can be described mathematically as a sum of a series of simple sine and cosine terms, which is the basis of the mathematical procedure called the Fourier transform (see Section 4.2). Thus the square wave, frequently used in electronic circuits, can be described as the sum of an infinite superposition of sine waves, using the general equation ... 

Electric circuits can be very complicated. For example, they may include series-connected sections, parallel-connected sections, or both. No matter how complex they are, the behaviours of these sections are governed by fundamental laws, which provide basic tools for the analysis of all the circuits. 

Thevenin s theorem states that a section of a linear circuit containing one or more sources and impedances can be replaced with an equivalent circuit model containing only one voltage source and one series-connected impedance, as shown in Figure 2.35. 

We have discussed in the above sections Faradaic impedance and the correlation between Faradaic impedance and kinetic parameters. In general, one desires to separate the Faradaic impedance from Rel and Cd. Now we will focus on the extraction of Zf and the kinetic parameters from direct impedance measurements. This is based on the transformation between equivalent circuits in series and equivalent circuits in parallel. 

For both damped (liquid) and undamped environments, the ideal oscillator circuit should precisely track either the series or parallel resonance (see Section... 

---