Electric Circuits 8th Edition 82

Electric Circuits 8th Edition 82 - rr grves-ol +...

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58 Simpte Resistjve Circuih \t'i 'ii i )" R, RO Rr n;c-ir-i" figurc 3.1 A Resjstors connected jn sedes. R, RO RS 3.1 Resistors in Series In Chapter 2, we said that when just two elements connect at a single node.lhey are said to be in series. Seri€\-connected circuit eternents canr lhe same cuffenr.The resi.rors in rhe circuil shown iD frg.3.t are con- necled in series. \ e can show lhal lhe.e fesistorc cafry lh; .ame currerr b\ applling Kirchhoffs currenl law to cacb node in rh; circuir.The scrics interconnection in Fig. 3.1 requires that is=4= i2=ir=ia: is= -i6= i. , (3.1) which states that if we know any one ofthe seven currents, we know them all. Thus we can redraw Fig.3.1 as shown in Fig.3.2, retainhg rhe idenrity of the single
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Unformatted text preview: rr grves-ol + i"Rr + irn2 + irR3 + j.Rj + lrR5 + trn6 + irRT:0, (3.2) z ' . = t " ( R 1 + R 2 + & + & + R s + R 6 + R ? ) . (3.3) h g f e Figure 3.2 A Series resistors with a sjngte unkno\i/n The significance of Eq.3.3 for calculating ir is that the seven resistors can be replaced by a single resistor whose numeiical value is the sum of the individual resistors. that is. R e q = R 1 + R 2 + R 3 + R 4 + R 5 + R 6 + R 7 \3.4) and h Figure 3.3 A A simplified version of the cjrcujt shown in Fig.3.2. (3.5) Thus we can redraw Fig.3.2 as sho$n in Fig.3.3. In general, if tr resistors a.re connected in series, the equivalenl sircle re.islor has a resrstance equal lo lhe sum ot lhe & re,i.rancir. or (3.6) Note that the resistanc of the equivalent resistor is always larset than !har ot lhe largcsl resi.tor in rhe series conneclion. Combining resistoc in series >...
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