Time-dependent resistors

The objective of this monograph is to describe and interpret the time dependence of the electrical response of dielectrics. Interpretation is difficult because the observable relationship between polarization and field is simple in the cases relevant for dielectric relaxation and because the measurements have relatively little information content. The response of the dielectric can be described by a set of linear differential equations and many models can be described which correspond to the same differential equations. When the dielectric relaxation of a given material has been measured the investigator is in the position of a man presented with a black box which has two terminals. He may apply alternating fields of various kinds and he may heat the box but he is not allowed to look inside. And he finds that the box behaves as if it contained a combination of capacitors and resistors. 

Consider the ionization chamber shown in Fig. 5.6. The two parallel plates make a capacitor with capacitance C, and with the resistor R an RC circuit is formed. A constant voltage Fq is applied on the plates. The time-dependent... 

A differentiating circuit consists of a capacitor and a resistor (Fig. 10.2). If a time-dependent voltage V it) is applied at the input, Eq. 10.10 relating the instantaneous values of the three voltages involved (Fig. 10.5) becomes... 

In [9], it is suggested to explicitly represent considered degradation phenomena in a nominal bond graph of the system once a mathematical model for them is available. However, if a mathematical model of a degradation process derived from first principles is not available, if a nominal parameter in the constitutive equation of an element is then replaced by a function of time so that measured data is fitted and can be extrapolated into the future, a bond graph representation might be a problem. If a resistance becomes time-varying as of sometime point to then this may be simply captured by a nonlinear modulated resistor. If the nominal capacitance Co in the constitutive equation q t) = Co e(t) of a capacitor is replaced by a time-dependent capacitance C t) then... 

Dpreamp(/) IS then fed into an electronic differentiator. The basic electronic circuit for differentiating time-dependent signals utilizes an operational amplifier, a resistor R, and a capacitor C. This electronic... 

Electrochemical systems are in general nonlinear which often makes analytical treatment of their kinetics prohibitively complex. Fortunately, in many cases where small voltage changes are involved, a linear approximation, equivalent to representing the electrochemical system as an electric network made of ideal resistors, capacitors and inductors, can be employed. The voltage response of resistances is not only linear but also time independent, and it follows Ohms law, i = V/R, where R is not only independent of i and E but also independent of time. However, the current/voltage dependence of such elements as capacitors and inductors is time dependent and expressed by differential equations... 

When the a.c. signal is first impressed, a time-dependent diffusion layer is created. As no net current flows, a steady state is set up after a few cycles. This coupled diffusion and electrochemical problem has been solved with the following result [8]. Assuming that the impedance can be expressed as a series combination of a resistor and a capacitor ... 

The electrical photo response to excitation with a weak laser pulse of 10 ps duration absorbed in the bulk of Si is measured as time-dependent voltage drop across the external resistor Rm. If the time elapsed after the laser pulse is short compared to the RC constant of the circuit, the measured signal can be interpreted as photovoltage. It can be interpreted as photocurrent if the elapsed time is long compared to the RC constant. Figure 4 shows the response of an n-Si electrode in the ns time window to the absorption of a laser pulse of 10 ps duration. The black shaded area in Fig. 3 illustrates the generation of electron-hole pairs by the incident hght inside of the Si material. 

Figure 1.62. (a) Diagrammatic view of the correlation circuit for photoconductivity cross-correlation measurement in (CH) on broadband microstrip lines, (b) Corresponding circuit diagram. The switches are modeled using the approximation of lumped elements with a static capacitance Cg and a resistor having a time-dependent conductance G(/) in parallel. Z is the characteristic impedance of the transmission lines. (Reprinted with permission from ref. 149)... 

Often it is desirable to control the time constant, independent of sensor, cable, and input capacitances. In such a case it is recommended to use a charge amplifier (Fig. 4). The current delivered by the piezoelectric element is directly transferred to the capacitor Cm and the resistor Rm, irrespective of the sensor and cable capacitances Cp-and Cc- Under these conditions, the time constant is easily adjusted to allow for low-frequency measurements, where the sensor signal now follows the time-dependent force dF(t)/CM-... 

Note that this problem is completely equivalent to the well-known electrical problem of charging a capacitor C through a resistor by an ac source with a voltage Uq sin t (see Fig.11.12). The time-dependent voltage across C and the resistor R2 parallel to C can be obtained from the equation... 

Investigations of conductivity of insulating polymers are very difficult due to very low values of the measured currents. Additionally the apparent values of resistivity p or conductivity a are time dependent because the measured current decreases with increasing time after application of the electric field. This effect is due to complex polarization phenomena which occur when a step-voltage is applied to the sample. The resistance and capacitance of the insulating polymer can be represented by equivalent circuits with different serial and parallel combinations of resistors and capacitors in order to model the time (or frequency) dependence of the current. Such simulations can he used for elucidation of the resistance component of the sample. 

In order to improve the slope compensation circuitry that depends upon a resistor to ground all the time, I will split this resistor between the secondary winding of the current transformer and after the rectifiers. I will double the value of the two resistors (150 ohms each), so that when the diodes are conducting, the net value is the same. 

Ohm s law, V=J R (voltage equals current times resistance), electricity has the same form as equation 9.1-14 which may be written as equation 9.1-15, where AP is the pressure differential, Q is the flow rate and resistance is given by equation 9.1-16, where t] is the viscosity of the fluid. Table 9.1-2 shows that the viscosity of liquids is highly temperature-dependent. Gases are much less temperature dependent because of the greater separation between molecules. If there are multiple discharge paths the equivalent resistance is the same as electrical resistors in... 

Depending on the value of the resistor, the motor will, in general, draw a heavier current then when started using star-delta or auto-transformer methods. The resistors must be rated to carry the limited motor starting current for the time they are in circuit. 

Because the response time of the detector depends on the thermal time constant of the detector element / electrode assembly, coupled with the electrical time constant of the device capacitance and load resistor - the response versus modulation frequency (f shows a typical l//m form. 

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