Applications
Electric circuits axe formed by interconnecting various devices. In electric circuit theory one prepares mathematical models of these devices; describes the interconnection also in a mathematical way, and wishes to determine the mathematical model of the
- PDF / 2,817,610 Bytes
- 32 Pages / 481.89 x 691.65 pts Page_size
- 80 Downloads / 175 Views
Applications
Section 2.1 Kirchhoff-equations; the basic problem of network analysis Electric circuits are formed by interconnecting various devices. In electric circuit theory one prepares mathematical models of these devices; describes the interconnection also in a mathematical way, and wishes to determine the mathematical model of the whole circuit from those of the devices and interconnection:
Modelling:
Devices
+
In terconnection
Network elements (e.g. resistors)
+
Structure of interconnection (e.g. graphs)
1
1
--
--
Electric circuits
1
Electric networks
For example, let us operate a usual electric lamp with u = 220 Volt, P = 100 Watt. This circuit has three devices; the energy source, the lamp and the wire. We model the energy source as a voltage source (with a given voltage u = 220 Volt, with no internal resistance, and hence with an arbitrary current), we model the lamp as a resistor (which has arbitrary voltage u and arbitrary current i, subject to the condition u = Ri only, where R is the resistance of the lamp, u 2 / P = 484 Ohm in our case), and we suppose that the wire has no effect whatsoever. Hence we describe the structure of interconnection by saying that the resistor is parallel to the voltage source. Then we obtain a network and applying some rule (e.g. that parallel devices have the same voltage) we can calculate that the current i of the resistor should be u/ R = 0.45 Amps. Our modelling assumptions are valid to a certain extent only (e.g. the energy source must have some internal resistance, the wire might have some effect, the resistance of the lamp is not a constant but depends on outside temperature etc.) but we accept them since the obtained results are in good agreement with possible measurements performed on the real circuit. Even the basic assumptions that modelling the devices is independent of the way of their interconnection and that modelling the interconnection is independent of the actual devices, are also valid to a certain extent only.
In what follows, we first consider networks composed of resistors, voltage and current sources (with respective notations in Fig. 2.1). All of them can be A. Recski, Matroid Theory and its Applications in Electric Network Theory and in Statics © Springer-Verlag Berlin Heidelberg 1989
38
Chapter 2 Applications
~resistor
_ -+9-+_voltage source
-
Data Loading...
