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www.GOALias.blogspot.comExactly as beforeI = I 1+ I 2+ I 3(3.46)and applying Ohm’s law to R 1, R 2and R 3we get,So thatV = I 1R 1, V = I 2R 2, V = I 3R 3(3.47)⎛ 1 1 1 ⎞I = I 1+ I 2+ I 3= V ⎜ + + R 1 R 2 R ⎟(3.48)⎝3⎠An equivalent resistance R eqthat replaces the combination, would besuch thatVI =Reqand hence1 1 1 1= + +R R R Req1 2 3CurrentElectricity(3.49)(3.50)We can reason similarly for any number of resistors in parallel. Theequivalent resistance of n resistors R 1, R 2. . . ,R nis1 1 1 1= + + ... +R R R Req1 2 n(3.51)These formulae for equivalent resistances can be used to find outcurrents and voltages in more complicated circuits. Consider for example,the circuit in Fig. (3.17), where there are three resistors R 1, R 2and R 3.R 2and R 3are in parallel and hence we can23replace them by an equivalent R eq betweenpoint B and C with1 1 1eqR R23R = +2 3or,=RR23 2 3R eqR2 + R3(3.52)23The circuit now has R 1and Reqin seriesand hence their combination can be123replaced by an equivalent resistance R eqwithR = R + R(3.53)123 23eq eq1If the voltage between A and C is V, thecurrent I is given byVVI = =123ReqR1+ ⎡⎣R2R3/( R2 + R3)⎤⎦( + R )V R2 3=RR + RR + RR1 2 1 3 2 3FIGURE 3.17 A combination of three resistors R 1,R 2and R 3. R 2, R 3are in parallel with anequivalent resistance 2323Req . R 1and Req are inseries with an equivalent resistance R 123eq .(3.54)109