Series circuit proportional

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. 

It is important to analyze this circuit with respect to selectivity let us assume that our black box contains the two resistors—one capacitor series circuit. Under what conditions will measured Y be proportional to the unknown G and not be disturbed by variations in R and C And correspondingly under what conditions will measured Y" be proportional to unknown C and not be disturbed by variations in R and G ... 

P, and T, are the pressure and temperature at one end and P2 and T2 refer to the other end, M is the molecular weight of the gas, R is the gas constant, and N is Avogardo s number. This equation applies in the above-mentioned (molecular flow) region, which commences at about 10 J torr. Of particular importance is the direct proportionality of the flow to the cube of the tube diameter. Thus, large-diameter tubing and large-bore stopcocks improve the pumping speed at low pressures. As with a series electrical circuit, the total impedance (proportional to 1 /q) is equal to the sum of the individual impedances, Eq. (2). 

In the series branch of the equivalent electrical circuit, Lq is proportional to the quartz inertial mass displaced by the shear oscillation, Cq is proportional to the energy stored in the quartz crystal during oscillation and Rq describes the energy frictional loses of the quartz crystal. 

A schematic of the apparatus is shown in Figure 2. The series resistor senses current. When the overall circuit RC (R and C are circuit resistance and capacitance, respectively) time constant is short compared with the voltage developed on the sensing resistor is proportional to the instantaneous... 

Figure 18-1 A pH meter gives the pH of the solution directly. When the electrode is dipped into a solution, the meter displays the pH. The pH meter is based on the glass electrode. This sensing device generates a voltage that is proportional to the pH of the solution in which the electrode is placed. The instrument has an electrical circuit to amplify the voltage from the electrode and a meter that relates the voltage to the pH of the solution. Before being used, a pH meter must be calibrated with a series of solutions of known pH.

Heat transfer coefficients (either U or h are like conductances in electricity the heat flux is proportional to them (like electrical current through a resistor is proportional to its conductance). The reciprocal of the heat transfer coefficients (1/6/ or 1/A) is like an electrical resistance. The formula above (relating MU to Mh s ) is like that relating the overall resistance of a circuit composed of three resistors in series the total resistance is the sum of each of the three individual resistances. 

The Lever oscillator [39], Fig. 16, allows the application of series resonance configurations with one-side quartz electrode grounding. Since the effect of parasitic capacitance is minimized and simple shielding is possible, this circuit configuration is especially suited for under-liquid QCM. Besides the series resonance frequency, the series resonance resistance Rs can be measured. For this purpose the Lever oscillator allows a largely transistor current gain-independent measurement of the resistance. An automatic level control provides a signal proportional to Rs. 

The emitter coupled oscillator (Fig. 17) is a circuit also providing one quartz crystal electrode grounded. For practical realization as a series resonance oscillator, a signal proportional to the current through the quartz crystal is amplified and fed back as a voltage. Since least gain is necessary for low impedance resonance, the resonance with the smallest impedance will preferably be excited. Phase condition is fulfilled for a frequency where the quartz crystal behavior is real, i.e., for/r. 

For most applications, an alternative is employed. Recall that, in measuring the resistance of a thermistor, a fixed resistor is normally connected in series with the sensor. If a constant-voltage source ( s) is used, the circuit current is inversely proportional to the total resistance. Then the relationship between the measured voltage drop across the fixed resistor and the thermistor temperature can be almost linear over a range of temperature. The linear part of this curve can be shifted along the temperature scale by changing the value of the fixed resistor. 

For an ideal photoelectrode, the equivalent circuit can be simplified to a resistor (R) and a capacitor (C) in series. The R represents the resistance of the semiconductor bulk (plus any series resistance from the electrode wires and the electrolyte), and the C represents the capacitance of the space charge region (Csc)- For an ideal system, a plot of 1/C versus electrode potential ( ) yields a straight line. The line is extrapolated to 1/C = 0. The x-intercept equals Eft, + kT/e and the slope is proportional to the charge carrier concentration or doping density (iVoopant), as shown by Eq. (6.2). This equation is obtained by substimting the relevant terms from Eq. (6.1). 

Figure 4.1.51. Impedance spectrum of a symmetrical cell with composite cathode on both sides, fitted to two different circuits. The solid lines show the total fit, while the dashed Unes show the impedances of the individual elements. The composite layer consists of Zr02 (8 mol% Y2O3) and Lao.ssSro.isMni.ioOi in equal proportions and the current collector is porous platinum paste. The measurement was made in air, at 850°C. The data were corrected for the series inductance of the measurement rig, determined in short circuit.

The photocurrent generates a signal voltage Vs = ph = L ph across the load resistor that is proportional to the absorbed radiation power over a large intensity range of several decades, as long as Vs < AEg/ (Fig. 4.85b). From the circuit diagram in Fig. 4.86 with the capacitance Cs of the semiconductor and its series and parallel resistances and Rp, one obtains for the upper frequency limit [4.107]... 

Cavendish made experiments to find what power of the velocity the resistance is proportional to . By resistance he meant the whole force which resists the current, and by velocity the strength of the current through unit cross-section of the conductor. In four different series of experiments with salt solutions in wide and narrow tubes, he found that the resistance varied very nearly as the first power of the velocity , and this result, found in January 1781, is really Ohm s law. His experiments on divided circuits also anticipated Kirchhoff s application of Ohm s law to them. These experiments, it should be noticed, were carried out with frictional electricity not with currents from a battery, and the current strength was determined by comparisons of the shocks given to the body, although Cavendish made use of electrometers in other researches. 

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