Voltage independent equation

For most inductors used in power conversion, if we reduce the current to zero, the field inside the core also goes to zero. Therefore, an implicit assumption of complete linearity is also usually made — that is, B and I are considered proportional to each other as shown in Figure 2-13 (unless of course the core starts saturating, at which point, all bets are off ). The voltage independent equation can then be expressed as any of the equations shown in the figure — in other words, this proportionality applies to the peak values of current and field,... 

Note that the voltage-independent equation is useful if for example we want to do a quick check to see if our core may be saturating. Suppose we are custom-designing our inductor. We have wound 40 turns on a core with an area of A = 2 cm2. Its measured inductance... 

If voltages are referred to hydrogen half-cell potentials, Eq = . The Pourbaix diagram is a plot of versus pH for solid, gaseous, and dissolved components in equilibrium. It is apparent that if m and n appear [Pg.524]

Applying Kiichhoff s voltage law to this circuit gives three independent equations. Thus, we may write, for the loop that contains the battery and i ,... 

C2.2.12 and Ae is the anisotropy in pennittivity in the nematic liquid crystal. Note that in equation (C2.2.16) the tlireshold voltage, that is the relevant quantity for display operation, is independent of cell thickness. 

The inverter may be a current source inverter, rather than a voltage source inverter (.Section 6.9.4) since it will be the rotor current that is required to be vtiried (equation (1.7)) to control the speed of a wound rotor motor, and this can be independently varied through the control of the rotor current. The speed and torque of the motor can be smoothly and steplessly controlled by this method, without any power loss. Figures 6.47 and 6.48 illustrate a typical slip recovery system and its control scheme, respectively. 

The quantities E°, E x, and Eed are independent of how die equation for the cell reaction is written. You never multiply the voltage by the coefficients of the balanced equation. 

Cliff and Lorimer (1975) used this equation to form the basis for X-ray microanalysis of thin foils, where the constant kAB contains all the factors needed to correct for atomic number differences. kAB varies with operating voltage, but is independent of sample thickness and composition if the two intensities are measured simultaneously. Its value can be determined experimentally with accuracy, using specimens of known composition. The value of kAB can be determined by calculation more rapidly, but with less accuracy. 

Equation (1) is the basis for using EIS capacitors or ISFETs to measure changes in Vo- If an ISFET is used, the measured quantity is the threshold voltage, which is equal to the flat-band voltage plus a constant. In both cases only variations of Vo can be measured, because the other terms in (1) are not independently known with sufficient accuracy. 

This same equation is, of course, also used to rationalise the general electronic behaviour of metals, semiconductors and insulators. The quantitative application of Eqn (2.1) is handicapped for ionic conductors by the great difficulty in obtaining independent estimates of c,- and u,-. Hall effect measurements can be used with electronic conductors to provide a means of separating c, and u,- but the Hall voltages associated with ionic conduction are at the nanovolt level and are generally too small to measure with any confidence. Furthermore, the validity of Hall measurements on hopping conductors is in doubt. 

Notice that when the silver reaction is multiplied by 2 its E° value stays the same. The potential of a half-cell does not depend on the coefficients of the equation because the potential of the cell is independent of the quantities of reactants. Adding the two half reactions gives the overall reaction and the cell voltage ... 

A pH measurement is usually taken by immersing a glass combination electrode into a solution and reading the pH directly from a meter. At one time, pH measurements required two electrodes, a pH-dependent glass electrode sensitive to H+ ions and a pH-independent calomel reference electrode. The potential difference that develops between the two electrodes is measured as a voltage as defined by Equation 2.2. 

In equation 21, fR is a constant current independent of the applied bias. Thus, the current increases exponentially with the applied voltage. This... 

At 1=0, in a steady state condition, the sensor voltage is a constant zero and is independent of the oxygen partial pressure in the exhaust gas. As shown in the calculated results (See Figure 10), both Po2(l) and P0g(o) depend on the air-fuel ratio. But Po2(l) is always equal to Po2(0) (See Equation 38) thus, E becomes zero (See Equation 39). In this case, the internal total pressure Pq1 is equal to 1 atm. Experimental data show on-off type sensor voltage characteristics in a rich atmosphere when a current is applied to the sensor. (See Figures 5 and 6)... 

Apparently, the current in the ascending part of the wave and the pseudo-limiting current are mostly determined by transport-independent, kinetic factors. The limiting current of the second wave, obtained after correction for the IR voltage drop, satisfies the Levich relation (Chapter 1, Equation 1.15) and is hence determined by the transport rate of hydrogen peroxide to the electrode surface. This wave will not be further discussed since it is of no use for the aim of this investigation. 

In closing, we see that certain simplified models are beneficial, especially when they permit analytical solutions to be derived showing the influence of all key governing parameters. As seen in the above analysis, however, certain information is unavailable such as information on the transient cell voltage. In addition, effort is needed to independently assess the overall cell resistance, R(I). which, in general, is also a function of other parameters (reactant concentration, temperature, and pressure). This can be remedied by adding additional equations as the following section shows. 

The equation (386) is not closed again and produces new Green functions of higher order. And so on. These sequence of equations can not be closed in the general case and should be truncated at some point. Below we consider some possible approximations. The other important point is, that average populations and lesser Green functions should be calculated self-consistently. In equilibrium (linear response) these functions are easy related to the spectral functions. But at finite voltage they should be calculated independently. 

---