A battery of emf ε$$0$$ $$=$$ $$12$$ V is connected across a $$4$$ m long uniform wire having resistance $$4$$ Ω$$/m$$. The cells of small emfs ε$$1$$ $$=$$ $$2$$ V and ε$$2$$ $$=$$ $$2$$ V having internal resistance $$2$$ Ω and $$6$$ Ω, respectively, are connected as shown in the figure. If galvanometer shows no deflection at the point N, the distance of point N from the point A is equal to

Question

A battery of emf ε$$0$$ $$=$$ $$12$$  V is connected across a $$4$$ m long uniform wire having resistance $$4$$  Ω$$/m$$. The cells of small emfs ε$$1$$ $$=$$ $$2$$  V and ε$$2$$ $$=$$ $$2$$  V having internal resistance $$2$$  Ω and $$6$$  Ω, respectively, are connected as shown in the figure. If galvanometer shows no deflection at the point N, the distance of point N from the point A is equal to

Infinity Learn · Accepted Answer

Potential gradient,$$x=128+16$$ × $$4$$ $$=$$ $$2$$  V  m−$$1Effective$$ emf of $$E1$$ and $$E2E=$$  $$E1r1$$ − $$E2r21/r1$$ $$+$$ $$1/r2=$$  $$12$$  voltBalancing length $$=$$  $$12$$   $$12$$  $$=$$  $$14$$  $$m=25$$  cm

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