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Question

A battery of emf E0=12 V is connected across a 4m long uniform wire having resistance 4 Ω/m. The cells of small emfs ϵ1=2V and ϵ2=4V 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
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A
16m
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B
13m
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C
25 cm
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D
50 m
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Solution

The correct option is C 25 cm
Voltage drop on the balancing length of the wireiρx
Here i=Current flowing in primary circuit
ρ=Resistance per unit length of the wire

x=Balancing length of wire AB when deflection in galvanometer is zero
1Req.(12+16)=46
Eeq.=(E1r1E2r2)1Req.=⎜ ⎜ ⎜224646⎟ ⎟ ⎟=12 volt
when deflection is zero E of secondary circuit=voltage drop across the wire AN
12=128+16×4×x
x=14 m.x=25 cm

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