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Unformatted text preview: . The equivalent resistance is
1
1
1
1
=
+
+ ··· +
Req
R1
R2
RN (2.38) Note that Req is always smaller than the resistance of the smallest resistor
in the parallel combination. If R1 = R2 = · · · = RN = R , then
R
(2.39)
N
For example, if four 100 resistors are connected in parallel, their equivalent resistance is 25 .
It is often more convenient to use conductance rather than resistance
when dealing with resistors in parallel. From Eq. (2.38), the equivalent
conductance for N resistors in parallel is
Req = Geq = G1 + G2 + G3 + · · · + GN (2.40) Conductances in parallel behave as a single conductance whose value is equal to the sum of the
individual conductances.  v v where Geq = 1/Req , G1 = 1/R1 , G2 = 1/R2 , G3 = 1/R3 , . . . , GN =
1/RN . Equation (2.40) states:  eText Main Menu  Textbook Table of Contents  Problem Solving Workbook Contents 44 PART 1 DC Circuits The equivalent conductance of resistors connected in parallel is the sum
of their individual conductances. i v a +
− v Req or Geq b Figure 2.32 Equivalent circuit to
Fig. 2.31. This means that we may replace the circuit in Fig. 2.31 with that in
Fig. 2.32. Notice the similarity between Eqs. (2.30) and (2.40). The
equivalent conductance of parallel resistors is obtained the same way
as the equivalent resistance of series resistors. In the same manner, the
equivalent conductance of resistors in series is obtained just the same way
as the resistance of resistors in parallel. Thus the equivalent conductance
Geq of N resistors in series (such as shown in Fig. 2.29) is
1
1
1
1
1
=
+
+
+ ··· +
Geq
G1
G2
G3
GN (2.41) Given the total current i entering node a in Fig. 2.31, how do we
obtain current i1 and i2 ? We know that the equivalent resistor has the
same voltage, or
iR1 R2
(2.42)
v = iReq =
R1 + R 2
Combining Eqs. (2.33) and (2.42) results in
i1 = i
i2 = i i1 = 0
R1 R2 = 0 i
i2 = 0 i1 = i
R1 R2 = ∞ (b) v v  (a) A shorted circuit,
(b) an open circuit.  i2 = R1 i
R1 + R 2 (2.43) which shows that the to...
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 Spring '12
 bkav

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