Series connected resistors

After direct current became available, attempts were made to use it in electrolytic conductance measurements. In 18 7, Eben Horsford (1818-1893) tried to allow for the effects of electrode polarization (J 0). He varied the length of the liquid path, then adjusted a calibrated series-connected resistor to restore the current to its original value. However, precise measurements of electrolytic conductance by d.c. methods had to await the perfection of the -electrode system by Gordon and his co-workers in the 19 0 s. 

With this technique the motor has a wound rotor brought out to slip rings and an external resistance is connected into the rotor circuit. This resistance usually consists of a series of resistor banks, which are switched out progressively in a number of steps as the motor accelerates. The number and rating of each step is chosen so that starting current and motor torque are within requirements. 

Figure 4.6a shows the circuit of a resistor and an inductor in series connection. Based on the primary rules, the overall impedance of this circuit is expressed as... 

Figure 4.6. a Resistor and inductor in series (Model D5) b Nyquist plot of resistor and inductor in series connection over the frequency range 1 MHz to 1 mHz (Model D5 R = 10 a, L = 0.0001 H)... 

Figure 2. Shot noise damping in a simple model circuit demonstrates why macroscopic linear conductors are usually free from this type of noise. The circuit is a series connection of N ideal current noise generators paralleled by ideal resistors. Anticorrelations in elementary transport events arise from the voltage fluctuations in connectors between generators.

In comparison to the BG in Fig.4.2, the BG in Fig.4.3 reproduced from [9] does not reflect the series connection of a resistor and a semiconductor switch. The latter one is not explicitly visible in the BG. Additional information must be known that junction I3 is a controlled junction. Moreover, detectors are not in inverted causality although sensors deliver a measured and thus known variable into a DBG. Also note that an auxiliary resistor R Rs2 is needed to determine the effort at junction O4. 

The Z-source DC circuit breaker basically consists of a silicon controlled rectifier (SCR) and two crossed L-C series connections. In case there is no fault, the SCR is on and the capacitors are charged by the voltage source. In steady state, the capacitor currents are zero, the voltages across the inductor vanish and a constant current fiows through the series connection of inductors and load. Suppose that the resistances of the inductors can be neglected and that the load is the parallel connection of a load resistor Rl and a load capacitor Cl - Then steady-state values are ... 

If there is a circuit consisting of a resistor and a capacitor in series connected to the voltage source V, the voltage applied to the system is the sum of the potentials on the resistance (ohmic drop) and on the capacitance ... 

The measurements on such a structure were done by constmcting a first-order passive high-pass filter and using the fabric sample as the capacitor series connected to a 1 MQ resistor. To verify the pressure sensor function, a sine signal with frequency 10 kHz and peak-to-peak amplitude 3 V was sent by a function generator to the textile sample (Fig. 28.31, left). The output signal was read on an oscilloscope. The distance... 

To elucidate the foregoing general statements let us consider the network sketched in Fig. 6.9 as an example. It basically consists of an ideal capacitor (Coo) and in parallel another capacitor (C) with a series connection to an ideal resistor (R). The capacitance (C ,) is proportional to the permittivity at very high (optical) frequencies of the applied electric field (s =n p,) which is... 

These systems (see Figure 11.11, top) are preferably applied in connection with gas-tight NiCd accumulators. Systems that operate in the microwatts range are sufficiently protected by a simple ohmic resistor, whereas for higher power ratings a series connection of transistors is advised. 

Studies of capacitance vs electric field at different sweeping rates were also carried out for MIS devices (see Fig. 21c). As evident from the Fig. 21c, the slower the scan rate, the larger is the hysteresis. Further, from the studies of the real part of impedance [45], Z and imaginary part of Z" of the MIS devices, it was found that a simple model based on series connection of two capacitors and resistors for the two layers cannot explain the observed phenomena (see Fig. 22). It gives an impression... 

Fig. 19 Equivalent circuit models for caibon-based porous electrodes RC circuits for a series and b parallel connections, representing an equivalent circuit (simplest) of a capacitor. R resistor, C capacitor. Equivalent circuits of only one capacitor (Cdl or CP) in parallel to a resistor R and in series to resistor RS (c) and considering both Cdl (in parallel to RE) and CP (in parallel to RE ) in series with RS (d) are also shown. The ac responses to the latter two circuits are shown in (e, f) [33] (Reprinted with permission from Ref. [33] Copyright (2012) by John Wiley and Sons)...

If the system behaves like an ohmic resistor, i.e., with Z = R, the applied voltage and the current are in phase, i.e., with a phase shift O = 0. If only a capacitance C is effective, the impedance equals the capacitive resistance Z = l/coC with a phase shift of O = ji/2 with CO = 27i/with the frequency/ An in-series connection of C and R requires the addition of both resistances ... 

If, however, VB is not correct, the voltage divider or the (T, R3, R4) amplifier or both may be defective. To disentangle responsibilities, remove the transistor and check VB again. If VB is near its nominal value, then the fault has to be attributed to (T, R3, R4). As T was removed, you have a very effective way of checking (R3, R4), Fig. 6.7. Connect in series with R3 and R4 a resistor of accurately known value and such that the current 1 flowing across the series connection R3, R, R4 ... 

Figures 5.29a and 5.29b show the Bode and Nyquist plot for a resistor, Ro, connected in series with a resistor, Rt, and capacitor, Ci, connected in parallel. This is the simplest model which can be used for a metal-solid electrolyte interface. Note in figure 5.29b how the first intersect of the semicircle with the real axis gives Ro and how the second intersect gives Ro+Rj. Also note how the capacitance, Ct, can be computed from the frequency value, fm, at the top of the semicircle (summit frequency), via C l JifmR .

Next, measure your resistors connected two at a time in series. This means that two of the resistors are connected end to end. When two resistors are connected in this fashion, the total resistance is the sum of the two. To do this, use the socket board and insert the wire ends of one resistor into sockets FI and F5 (as in step 5), for example, so that the ends are not connected internally. Then insert the wire ends of the other resistor into sockets G5 and G9, for example. Since G5 and F5 are connected internally, this connects both resistors in series. Now measure the total resistance by touching the lead tips of the multimeter to sockets HI and H9. Record the individual values of the two resistors, the sum of the two, and the measured value of the sum in another table (four columns) in your notebook. Repeat with several different combinations. Comment on the agreement (or lack thereof) between the calculated and measured values. 

Construct a complete circuit with a battery and two resistors in series. To do this, choose the two resistors you want to use and connect them in series on the socket board, as in step 6. Then,... 

The electronic circuit of the safety sensor consists of a p-type silicon electrode, an LED, a resistor, two 3 V lithium batteries, and a platinum wire as a counter electrode, connected in series, as shown in the right part of Fig. 10.7. These components are assembled in a pen-like housing, optimized to measure even thin layers of liquid on a flat surface, as shown in the left part of Fig. 10.7. This configuration is advantageous if a puddle, observed for example under a wet bench or other equipment, is to be analyzed. 

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