Chapter 1 Electrical Fundamentals Review 7 Copyright Goodheart-Willcox Co., Inc. Arranging elements in a parallel circuit is far more practical than arranging them in a series circuit. Devices are subject to almost no adverse effects from other elements, as is the case with series circuits. 1.2.3 Complex Circuits Most circuits are not simply series or parallel, but a complex arrangement consisting of series and parallel portions. A series-parallel combi- nation circuit can be broken down into an equivalent circuit by applying the concepts mentioned previously. (c) Formula: 1 __ RT = 1 __ R1 + 1 __ R2 + 1 __ R3 (c) Solution: 1 __ RT = 1 ___ 10 Ω + 1 ___ 30 Ω + 1 ___ 20 Ω = 6 __ 60 + 2 __ 60 + 3 __ 60 = 11 __ 60 = 0.18333 R T = 60 __ 11 = 1 ____ 0.18333 = 5.45 Ω SAMPLE PROBLEM 1-3 Problem: Refer to the following complex cir- cuit. The source voltage is 12 volts. What is the (a) total resistance, (b) total current, and (c) volt- age across each resistor? 12 V R1 = 1 Ω R2 = 7 Ω R3 = 6 Ω R4 = 12 Ω (Continued) (a) Formulas: 1 __ R EQ = 1 __ R 3 + 1 __ R 4 R T = R 1 + R 2 + R EQ (a) Solution: Think of the circuit as a series cir- cuit where R 1 is the fi rst resistor, R 2 is the second, and R 3 and R 4 combine to make the third resistor. 12 V R1 R2 R4 REQ R3 The total resistance of the two parallel branches (R 3 and R 4 ) is the equivalent resistance. The equivalent voltage is the total voltage in the parallel branches. 1 __ R EQ = 1 __ 6 Ω + 1 ___ 12 Ω = 2 __ 12 Ω + 1 __ 12 Ω = 3 ___ 12 Ω = 1 __ 4 Ω R EQ = 4 Ω R T = 1 Ω + 7 Ω + 4 Ω = 12 Ω (b) Formulas: I T = E T __ R T (b) Solution: I T = 12 V ___ 12 Ω = 1 A (c) Formulas: I 1 = I 2 = I EQ = I T E 1 = I 1 R 1 E 2 = I 2 R 2 (Continued)