Fundamental Electrical and Electronic Principles, Third Edition

56 Fundamental Electrical and Electronic PrinciplesB(I 1 I 3 )IAI 1I 2R 1 R 3I 3CR 5RR 42(I 2 I 3 )DE 1Fig. 2.23Notice that although there are five resistors, the current law has beenapplied so as to minimise the number of ‘ unknown ’ currents to three.Thus only three simultaneous equations will be required for thesolution, though there are seven possible loops to choose from. Theseseven loops are:ABCDA; ADCA; ABDCA; ADBCA; ABDA; BCDB; andABCDAIf you trace around these loops you will find that the last three do notinclude the source of emf, so for each of these loops the sum of theemfs will be ZERO! Up to a point it doesn ’ t matter which three loopsare chosen provided that at least one of them includes the source.If you chose to use only the last three ‘ zero emf ’ loops you wouldsucceed only in proving that zero equals zero!The present level of study does not require you to solve simultaneousequations containing three unknowns. It is nevertheless good practicein the use of Kirchhoff’s laws, and the seven equations for the aboveloops are listed below. In order for you to gain this practice it issuggested that you attempt this exercise before reading further, andcompare your results with those shown below.ABCA : E 1 I 1 R 1 ( I 1 I 3 ) R 3ADCA : E 1 I 2 R 2 ( I 2 I 3 ) R 4ABDCA : E 1 I 1 R 1 I 3 R 5 ( I 2 I 3 ) R 4ADBCA : E 1 I 2 R 2 I 3 R 5 ( I 1 I 3 ) R 3ABDA : 0 I 1 R 1 I 3 R 5 I 2 R 2BCDB : 0 ( I 1 I 3 ) R 3 ( I 2 I 3 ) R 4 I 3 R 5ABCDA : 0 I 1 R 1 ( I 1 I 3 ) R 3 ( I 2 I 3 ) R 4 I 2 R 2