6 Modern Commercial Wiring Copyright Goodheart-Willcox Co., Inc. a parallel circuit. In electrical circuits, the term parallel does not necessarily mean physically or geometrically parallel, but merely signifi es alternate routes or branches. Parallel circuits are often called branched circuits. The following lists some of the characteristics of parallel circuits: • The voltage across all branches of the circuit is the same as the total voltage at the source. E TOTAL = E A = E B = E C = E N • The total current is equal to the sum of the currents fl owing through each of the branches. I TOTAL = I A + I B + I C + … + I N • The total resistance in a parallel circuit is the reciprocal of the sum of the reciprocals of the separate branch resistance. To express this in a much clearer manner, let us look at it mathematically: 1 ___ R TOTAL = 1 __ R 1 + 1 __ R 2 + 1 __ R 3 + … + 1 __ R N • Ohm’s law applies to the entire circuit and any of the branches. • Any opening or break of a branch does not stop the current fl ow through other branches. For this reason, parallel circuits have a distinct advantage over series circuits. Notice that the characteristics of a parallel cir- cuit are in many ways opposite those of a series circuit. The following example illustrates the relationships at work in a parallel circuit. Source R1 R2 R3 Goodheart-Willcox Publisher Figure 1-6. Current moves through parallel circuits using more than one pathway. SAMPLE PROBLEM 1-2 Problem: Using the following fi gure, fi nd (a) the current through each resistor, (b) the total current of the circuit, and (c) the total circuit resistance. 120 V Source R1 = 10 Ω R3 = 20 Ω R2 = 30 Ω (a) Formulas: E T = E 1 = E 2 = E 3 I 1 = E 1 __ R 1 I 2 = E 2 __ R 2 (a) Solution: E T = E 1 = E 2 = E 3 = 120 V I 1 = 120 V ___ 10 Ω = 12 A I 2 = 120 V ___ 30 Ω = 4 A I 3 = 120 V ___ 20 Ω = 6 A (b) Formula: I T = I 1 + I 2 + I 3 (b) Solution: I T = 12 A + 4 A + 6 A = 22 A (Continued)