# 231 is known as a current divider notice that the

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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. (2.43) becomes G1 i1 = i (2.44a) G1 + G 2 i2 = | Textbook Table of Contents | G2 i 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 current Gn i (2.45) in = 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. Solution: 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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