In a meter bridge , the wire of length $$1$$ m has a $$non-uniform$$ $$cross-section$$ such that, the variation dRdl of its resistance R with length l is dRdlα$$1l$$ , two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP ?

Question

In a meter bridge , the wire of length $$1$$ m has a $$non-uniform$$ $$cross-section$$ such that, the variation dRdl of its resistance R with length l is dRdlα$$1l$$ , two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP ?

Infinity Learn · Accepted Answer

For the given wire ; $$dR=Cdll$$ where $$c=constant$$  Let resistance of part AP and PB is $$R1$$ and $$R2$$  resp. Now,   ∫$$dR=C$$∫dll $$R1=C$$∫$$0ll$$−$$1/2dl=C.2$$.l $$R2=C$$∫$$l1l$$−$$1/2dl=2C.1$$−l Putting $$R1=R2$$ $$C2l=2C1$$−l ⇒$$2l=1$$ ⇒$$l=1/2$$ ⇒$$l=1/4m=0.25m$$

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