Unformatted text preview: tal current i is shared by the resistors in inverse
proportion to their resistances. This is known as the principle of current
division, and the circuit in Fig. 2.31 is known as a current divider. Notice
that the larger current ﬂows through the smaller resistance.
As an extreme case, suppose one of the resistors in Fig. 2.31 is zero,
say R2 = 0; that is, R2 is a short circuit, as shown in Fig. 2.33(a). From
Eq. (2.43), R2 = 0 implies that i1 = 0, i2 = i . This means that the
entire current i bypasses R1 and ﬂows through the short circuit R2 = 0,
the path of least resistance. Thus when a circuit is short circuited, as
shown in Fig. 2.33(a), two things should be kept in mind:
1. The equivalent resistance Req = 0. [See what happens when
R2 = 0 in Eq. (2.37).] (a) Figure 2.33 R2 i
R1 + R 2 e-Text Main Menu 2. The entire current ﬂows through the short circuit.
As another extreme case, suppose R2 = ∞, that is, R2 is an open
circuit, as shown in Fig. 2.33(b). The current still ﬂows through the path
of least resistance, R1 . By taking the limit of Eq. (2.37) as R2 → ∞, we
obtain Req = R1 in this case.
If we divide both the numerator and denominator by R1 R2 , Eq.
G1 + G 2
i2 = | Textbook Table of Contents | G2
G1 + G 2 (2.44b) Problem Solving Workbook Contents CHAPTER 2 Basic Laws 45 Thus, in general, if a current divider has N conductors (G1 , G2 , . . . , GN )
in parallel with the source current i , the nth conductor (Gn ) will have
G1 + G 2 + · · · + GN
In general, it is often convenient and possible to combine resistors
in series and parallel and reduce a resistive network to a single equivalent
resistance Req . Such an equivalent resistance is the resistance between
the designated terminals of the network and must exhibit the same i -v
characteristics as the original network at the terminals. EXAMPLE 2.9
4Ω Find Req for the circuit shown in Fig. 2.34.
To get Req , we combine resistors in series and in parallel. The 63- resistors are in parallel, so their equivalent resistance is and...
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