CHAP. 3]

CIRCUIT LAWS

25

Starting at the lower left corner of the circuit, for the current direction as shown, we have va þ v1 þ vb þ v2 þ v3 ¼ 0 va þ iR1 þ vb þ iR2 þ iR3 ¼ 0 va  vb ¼ iðR1 þ R2 þ R3 Þ

3.3

KIRCHHOFF’S CURRENT LAW

The connection of two or more circuit elements creates a junction called a node. The junction between two elements is called a simple node and no division of current results. The junction of three or more elements is called a principal node, and here current division does take place. Kirchhoﬀ’s current law (KCL) states that the algrebraic sum of the currents at a node is zero. It may be stated alternatively that the sum of the currents entering a node is equal to the sum of the currents leaving that node. The node voltage method of circuit analysis introduced in Section 4.3 is based on equations written at the principal nodes of a network by applying Kirchhoﬀ’s current law. The basis for the law is the conservation of electric charge. EXAMPLE 3.2.

Write the KCL equation for the principal node shown in Fig. 3-2. i1  i2 þ i3  i4  i5 ¼ 0 i1 þ i3 ¼ i2 þ i4 þ i5

Fig. 3-2

3.4

CIRCUIT ELEMENTS IN SERIES

Three passive circuit elements in series connection as shown in Fig. 3-3 have the same current i. The voltages across the elements are v1 , v2 , and v3 . The total voltage v is the sum of the individual voltages; v ¼ v1 þ v2 þ v3 .

Fig. 3-3

If the elements are resistors,

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An