# For n resistors in series then n req r1 r2 rn

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Unformatted text preview: r of resistors connected in series is the sum of the individual resistances. Resistors in series behave as a single resistor whose resistance is equal to the sum of the resistances of the individual resistors. For N resistors in series then, N Req = R1 + R2 + · · · + RN = Rn (2.30) n=1 To determine the voltage across each resistor in Fig. 2.29, we substitute Eq. (2.26) into Eq. (2.24) and obtain v1 = R1 v, R1 + R 2 v2 = R2 v R1 + R 2 (2.31) Notice that the source voltage v is divided among the resistors in direct proportion to their resistances; the larger the resistance, the larger the voltage drop. This is called the principle of voltage division, and the circuit in Fig. 2.29 is called a voltage divider. In general, if a voltage divider has N resistors (R1 , R2 , . . . , RN ) in series with the source voltage v , the nth resistor (Rn ) will have a voltage drop of vn = Rn v R1 + R2 + · · · + RN (2.32) 2.6 PARALLEL RESISTORS AND CURRENT DIVISION Consider the circuit in Fig. 2.31, where two resistors are connected in parallel and therefore have the same voltage across them. From Ohm’s law, | v v v = i1 R1 = i2 R2 | e-Text Main Menu | Textbook Table of Contents | Problem Solving Workbook Contents CHAPTER 2 Basic Laws 43 or i v v i1 = , i2 = R1 R2 Applying KCL at node a gives the total current i as Node a (2.33) i2 i1 v i = i1 + i2 + − R2 R1 (2.34) Substituting Eq. (2.33) into Eq. (2.34), we get i= v v + =v R1 R2 1 1 + R1 R2 = v Req Node b (2.35) Figure 2.31 Two resistors in parallel. where Req is the equivalent resistance of the resistors in parallel: 1 1 1 = + Req R1 R2 (2.36) or 1 R1 + R2 = Req R1 R2 or Req = R1 R 2 R1 + R 2 (2.37) Thus, The equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum. It must be emphasized that this applies only to two resistors in parallel. From Eq. (2.37), if R1 = R2 , then Req = R1 /2. We can extend the result in Eq. (2.36) to the general case of a circuit with N resistors in parallel...
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