# Electrical engineers handbook by Wai-Kai Chen

By Wai-Kai Chen

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1 (B) A Directed Graph Graphs: Easy Pictorial Representations graph, the edge (vi , vj ) is said to be incident out of vi and is said to be incident into vj . Vertices vi and vj are adjacent if an edge connects vi and vj . The number of edges incident on a vertex vi is called the degree of vi and is denoted by d(vi ). In a directed graph, din (vi ) refers to the number of edges incident into the vertex vi , and it is called the in-degree. In a directed graph, dout (vi ) refers to the number of edges incident out of the vertex vi or the outdegree.

It is often convenient to represent paths and circuits by the sequence of edges representing them. 3 e4 V2 e1 e6 e5 V5 e9 e7 V3 e2 V4 (B) A Directed Graph Graphs Showing Paths e2 , e3 , e4 , e5 , e6 is a circuit. 3(B) P: e1 , e2 , e7 , e5 is a directed path and C: e1 , e2 , e7 , e6 is a directed circuit. Note that C: e7 , e5 , e4 , e1 , e2 is a circuit in this directed graph, although it is not a directed circuit. Similarly, P: e9 , e6 , e3 is a path but not a directed path. A graph is connected if there is a path between every pair of vertices in the graph; otherwise, the graph is not connected.

By definition, the reactive power taken by an inductor is positive, and the reactive power taken by a capacitor is negative. Complex power representation is useful in calculating the power supplied by the source to a number of loads connected in the system. Power factor is defined as the ratio of the average power in an ac circuit to the apparent power, which is the product of the voltage and current magnitudes. power factor ¼ average power P ¼ apparent power S (1:77) Power factor (PF) has a value between zero and unity.