Kirchoffs current law

It is usual to define the primary beam current the BSE current /rse, the SE current and the sample current transmitted through the specimen to ground such that the Kirchoff current law holds ... 

Second, the Kirchoff current law applied to the node of potential B yields... 

FIGURE 15.1 The steps involved for the application of MFA. First a suitable biochemical network is obtained from the literature or from direct experimentation. Some metabolic fluxes are measured, either directly or by isotopomer techniques. MFA is then used to estimate the values of the unmeasured fluxes in the network based upon the measured metabolic fluxes in a manner analogous to KirchofFs current law. 

These observations, and application of Kirchoff s law, suggest that the time dependent electrochemical current density, Je(t), may be written as the product of the fractional intermediate surface coverage, 6 t(t), and the difference between the photo-generation and recombination current densities, JL(t) and Jr(t), respectively. Thus ... 

Details of the solution methods for electrical circuits by the Maxwell loop currents, A-Y conversions, and the Kirchoff current and voltage laws are assumed to be known to the student Otherwise, refer to a standard textbook on electrical circuit theory. 

To have a better appreciation of the utility of these representations let us first consider the laws that govern flow rates and pressure drops in a pipeline network. These are the counterparts to Kirchoffs laws for electrical circuits, namely, (i) the algebraic sum of flows at each vertex must be zero (ii) the algebraic sum of pressure drops around any cyclic path must be zero. For a connected network with N vertices and P edges there will be (N — 1) independent equations corresponding to the first law (Kirchoffs current... 

Thus, for a constant field, the flux of current density through a closed surface is always zero, that is, the amount of charge arriving in a volume during a given time period is exactly equal to the amount of charge that leaves that volume in the same period. Let us note that the last equation in set 1.136 is the well-known Kirchoff s law for currents. 

The same basic circuit can be extended further. Through use of Kirchoff s current law at the negative input, a number of voltage signals can undergo a weighted summation process as shown in Figure 274. 

Now, if we replace R2 with a capacitance C, we have a frequency-dependent component that allows, via Kirchoff s current law at the inverting input, to state that... 

Through applications of voltage division and Kirchoff s current law, a straightforward algebraic manipulation reveals amplification of the difference voltage ( 2 - Ui) as follows ... 

Another basic and equally important principle is Kirchoff s current law, which states that the electric current entering any point in a circuit must always be equal to the current leaving that point in the circuit. In the light of the definition of electric current as the movement of electrons from point to point through a conductive pathway, this law seems concrete and obvious. It is interesting to note, however, that it was devised in 1845, well before the identification of electrons as discrete particles and the discovery of their role in electric current. 

Kirchoff s current law was stated before electrons were discovered and identified, and electricity was still regarded as some kind of mysterious fluid that certain materials contained. 

Kirchoff s Law At any point in a circuit, there is as much current flowing into the point as there is flowing... 

Using Kirchoff s Current Law from electrical circuit theory. 

Fig. 21 The variation of the balancing tunneling current of the four branches four electrodes monomolecular Wheatstone bridge connected as presented in (a). In (b), the dashed line is for the current intensity 7W (in absolute value) measured by the ammeter A and deduced from the standard Kirchoff laws calculating each molecular wire tunneling junction resistance of the bridge one after the other from the EHMO-ESQC technique. In (b), Hie full line is the same tunnel current intensity but obtained with the new intramolecular circuit rules discussed in Sect. 2. (c) The resistance of the branch used to balance the bridge as a function of its rotation angle. The minimum accessible resistance by rotation is 78 MQ for the short tolane molecular wire used here...

The Hagen-Poiseuille law is mathematically analogous to the Ohm s Law. In addition, the conservation of mass (or flow for incompressible fluid) of fluid is analogous to the law of conservation of charge and current in electrical systems. This analogy allows for the use of Kirchoffs equations for calculation of the distribution of the volumetric flow of liquid between channels in a microfluidic network once we know the resistances of all the channels in the network and the pressures at the inlet and outlet, we can calculate the speed of flow in any part of the network (Fig. 1). 

The equivalent circuit, which is essentially a resistive network, provides a set of simultaneous equations derived by applying Kirchoff s node and loop laws. Thus, at a node, the algebraic sum of electric currents flowing in and out is zero, and in a closed circuit of network, the sum of the ohmic voltages (with respect to the direction of the current) is equal to the sum of the voltage sources. These equations, expressed in... 

The direction of the three currents shown in Fig. 10.3 has been arbitrarily assumed. If any turns out to be negative, this means that the current is actually in the opposite direction to that assumed. The three currents may be found by application of KirchofFs laws. 

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