Q. A battery of emf E0 = 12V is connected across a 4m long uniform wire having resistance 4Ω/m. The cell of small emfs e1 = 2V and e2 = 4V having internal resistance 2Ω and 6Ω 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
(a) 5/3 m
(b) 4/3 m
(c) 3/2 m
(d) None of these
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Ans: (d)
Sol: Current $ \displaystyle I = \frac{E_0}{4+16} $
$ \displaystyle I = \frac{12}{20} = 0.6 A$
$ \displaystyle V_{AB} = 12- 4 \times 0.6 = 9.6 V$
Potential gradient k = VAB/L = 9.6/4 = 2.4v/m
Net emf $ \displaystyle E_{eq} = \frac{E_1/r_1 + E_2/r_2}{1/r_1 +1/r_2} $
$ \displaystyle E_{eq} = \frac{2/2 + 4/6}{1/2 + 1/6} = 2.5 V $
As E = k l
l = Eeq/k = 2.5/2.4 = 25/24