Chapter 1 Electrical Fundamentals Review 5 Copyright Goodheart-Willcox Co., Inc. The following example illustrates the charac- teristics and relationships of a series circuit and how Ohm’s law is used to solve circuit problems. Series circuits are rarely encountered in prac- tical commercial, residential, or industrial wir- ing applications. These circuits have several inherent problems: • Any change of a resistance in the circuit affects the current throughout the circuit. This, in turn, changes the voltage across the other resistors in the circuit. • If any part of the path is broken (opened), the circuit is dead. If one element fails, the entire circuit is shut off. • Switches or other controlling devices cannot be used for individual loads within the circuit. If one load is turned off, all loads lose power. • Voltage across any load depends on the overall circuit arrangement. It is almost impossible to design circuit devices that can operate at so many different voltages. 1.2.2 Parallel Circuits A parallel circuit is one in which the elements are arranged in such a manner that there are sev- eral paths for the current. Figure 1-6 illustrates SAMPLE PROBLEM 1-1 Problem: Using the following fi gure, calculate the current fl owing through the circuit and the voltage at each resistor. 120 V Source R1 = 20 Ω R3 = 30 Ω R2 = 10 Ω Formulas: IT = E T __ R T R T = R 1 + R 2 + R 3 IT = I1 = I2 = I3 E N = I N R N = I T R N Solution: The current can be calculated using the formula IT = E T __ R T To fi nd the total resistance, add the individual resistances together: R T = R 1 + R 2 + R 3 = 20 Ω + 10 Ω + 30 Ω = 60 Ω The voltage is 120 volts, so the current is I T = 120 V ___ 60 Ω = 2 A The voltage at each resistor can be calculated using the fact that current is constant through- out the circuit: I 1 = I 2 = I 3 = I T (Continued) Therefore, E 1 = I 1 R 1 = I T R 1 = 2 A × 20 Ω = 40 V E 2 = I 2 R 2 = I T R 2 = 2 A × 10 Ω = 20 V E 3 = I 3 R 3 = I T R 3 = 2 A × 30 Ω = 60 V The current fl owing through the circuit is 2 amps, with resistor voltages of 40 volts (E 1 ), 20 volts (E 2 ), and 60 volts (E 3 ).