8 Modern Commercial Wiring Copyright Goodheart-Willcox Co., Inc. Notice in Sample Problem 1-3 how the sum- mation of the voltage across each of the resistors within the equivalent series circuit is equal to the source voltage. The power is also conserved: P T = E T I T = 12 V × 1 A = 12 W P 1 + P 2 + P EQ = E 1 I 1 + E 2 I 2 + E EQ I EQ = (1 V × 1 A) + (7 V × 1 A) + (4 V × 1 A) = 1 W + 7 W + 4 W = 12 W E EQ = I EQ R EQ E 3 = E 4 = E EQ (c) Solution: I 1 = I 2 = I EQ = 1 A E 1 = 1 A × 1 Ω = 1 V E 2 = 1 A × 7 Ω = 7 A E EQ = 1 A × 4 Ω E 3 = 4 V E 4 = 4 V The two power values are equal. The various characteristics of electric circuits are summa- rized in Figure 1-7. 1.3 Alternating Current Alternating current (ac) has current constantly changing direction and voltage continuously changing value and polarity. Therefore, just understanding voltage, current, and resistance is not enough (as it is with direct current). We must be familiar with how alternating current is generated and its inherent characteristics and relationships. Alternating current is produced by genera- tors and then distributed by a vast transmis- sion system to plants, commercial buildings, and homes. Alternating current is easier and less costly to generate than direct current (dc) and is conveniently distributed. In addition, the voltage and current can be altered using transformers to suit specifi c requirements. 1.3.1 Electromagnetic Induction When a conductor is moved across a mag- netic fi eld, as shown in Figure 1-8, an electromagnetic force is produced in the conductor. If the conductor forms a closed loop (circuit), the emf will cause a current to fl ow around this loop. This is referred to as electromagnetic induction. Goodheart-Willcox Publisher Figure 1-7. Summary of the characteristics of electrical circuits. Circuit Characteristics Series Circuits Parallel Circuits Complex Circuits Resistance Symbol: R Unit: Ohm (W) Sum of individual resistances R T = R 1 + R 2 + R 3 + … + R N Total resistance equals resistance of parallel portion and sum of series resistors. Current Symbol: I Unit: Ampere (A) The same throughout the entire circuit IT = I1 = I2 = I3 = … = IN Sum of individual currents IT = IA + IB + IC + … + IN Series rules apply to series portion of the circuit. Parallel rules apply to parallel part of the circuit. Voltage Symbol: E Unit: Volt (V) Sum of individual voltages E T = E 1 + E 2 + E 3 + … + E N Total voltage and branch voltage are the same E T = E A = E B = E C = … = E N Total voltage is sum of voltage drops across each resistor and each of the branches of the parallel portion. 1 __ R T = 1 __ R 1 + 1 __ R 2 + 1 __ R 3 + ... + 1 __ R N