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www.GOALias.blogspot.comstandard known resistance S. The jockey is connected to some point Don the wire, a distance l cm from the end A. The jockey can be movedalong the wire. The portion AD of the wire has a resistance R cml, whereR cmis the resistance of the wire per unit centimetre. The portion DC ofthe wire similarly has a resistance R cm(100-l).The four arms AB, BC, DA and CD [with resistances R, S, R cml andR cm(100-l)] obviously form a Wheatstone bridge with AC as the batteryarm and BD the galvanometer arm. If the jockey is moved along the wire,then there will be one position where the galvanometer will show nocurrent. Let the distance of the jockey from the end A at the balancepoint be l= l 1. The four resistances of the bridge at the balance point thenare R, S, R cml 1and R cm(100–l 1). The balance condition, Eq. [3.83(a)]givesR R l lS R l lcm 1 1= =cm ( 100 – 1)100 –(3.85)1Thus, once we have found out l 1, the unknown resistance R is knownin terms of the standard known resistance S byRl1= S100 – l(3.86)1By choosing various values of S, we would get various values of l 1,and calculate R each time. An error in measurement of l 1would naturallyresult in an error in R. It can be shown that the percentage error in R canbe minimised by adjusting the balance point near the middle of thebridge, i.e., when l 1is close to 50 cm. (This requires a suitable choiceof S.)CurrentElectricityExample 3.9 In a metre bridge (Fig. 3.27), the null point is found at adistance of 33.7 cm from A. If now a resistance of 12Ω is connected inparallel with S, the null point occurs at 51.9 cm. Determine the valuesof R and S.Solution From the first balance point, we getR 33.7S = (3.87)66.3After S is connected in parallel with a resistance of 12Ω , the resistanceacross the gap changes from S to S eq, where12SSeq=S + 12and hence the new balance condition now gives( + 12)51.9 R R S= =48.1 S 12 S(3.88)eqSubstituting the value of R/S from Eq. (3.87), we get51.9 S + 12 33.7= g48.1 12 66.3which gives S = 13.5Ω. Using the value of R/S above, we getR = 6.86 Ω.EXAMPLE 3.9121