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www.GOALias.blogspot.comimmediately gives us the relations I 1= I 3and I 2= I 4. Next, we applyKirchhoff’s loop rule to closed loops ADBA and CBDC. The firstloop gives–I 1R 1+ 0 + I 2R 2= 0 (I g= 0) (3.81)CurrentElectricityand the second loop gives, upon using I 3= I 1, I 4= I 2I 2R 4+ 0 – I 1R 3= 0 (3.82)From Eq. (3.81), we obtain,I1 R2=I2 R1whereas from Eq. (3.82), we obtain,I1 R4=I2 R3Hence, we obtain the conditionR2 R4= [3.83(a)]R1 R3This last equation relating the four resistors is called the balancecondition for the galvanometer to give zero or null deflection.The Wheatstone bridge and its balance condition provide a practicalmethod for determination of an unknown resistance. Let us suppose wehave an unknown resistance, which we insert in the fourth arm; R 4isthus not known. Keeping known resistances R 1and R 2in the first andsecond arm of the bridge, we go on varying R 3till the galvanometer showsa null deflection. The bridge then is balanced, and from the balancecondition the value of the unknown resistance R 4is given by,R2R4 = R3R[3.83(b)]1A practical device using this principle is called the meter bridge. Itwill be discussed in the next section.FIGURE 3.25Example 3.8 The four arms of a Wheatstone bridge (Fig. 3.26) havethe following resistances:AB = 100Ω, BC = 10Ω, CD = 5Ω, and DA = 60Ω.FIGURE 3.26EXAMPLE 3.8119