This preview shows page 1. Sign up to view the full content.
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
R1 + R 2 v2 = R2
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
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
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
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:
R2 (2.36) or
R1 + R2
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...
View Full Document
- Spring '12