# Network Equations

## 2.1 ELEMENTS AND NETWORKS

For our purposes, an element is a two-terminal electrical device. An electrical network, or circuit is a system consisting of a set of elements and a set of nodes, where every element terminal is identified with a unique node, and every node is identified with at least one element terminal. A network is completely connected, i.e., there is always at least one path from one node to another. Thus, an electrical network can be represented by a graph whose vertices correspond to circuit nodes and edges correspond to circuit elements. We distinguish between two types of elements, passive and active.

### 2.1.1 Passive Elements

A passive element is an element with the property that the voltage across it, v(t), and the current through it, i(t), may be related through a functional relationship of the form:

where f : , and where i′(t) and v′(t) are the first-order derivatives of i(t) and v(t), respectively. The functional relationship (2.1) is called the element equation. When the element equation does not depend on the derivative, so that ...

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