A battery of emf E0 = 12V is connected across a 4m long uniform wire having resistance 4Ω/m. The cell of small emfs…..

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

Current Electricity

(a) 5/3 m

(b) 4/3 m

(c) 3/2 m

(d) None of these

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

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