A battery of emf \( \varepsilon_{0}=12 \mathrm{~V} \) is connected across a \( 4 \mathrm{~m} \) ...

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A battery of emf \( \varepsilon_{0}=12 \mathrm{~V} \) is connected across a \( 4 \mathrm{~m} \) long uniform wire having resistance \( 4 \Omega / \mathrm{m} \). The cells of small emfs \( \varepsilon_{1}=2 \mathrm{~V} \) and \( \varepsilon_{2}=4 \mathrm{~V} \) having internal resistance \( 2 \Omega \) and \( 6 \Omega \) 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) \( \frac{1}{6} \mathrm{~m} \)
(b) \( \frac{1}{3} \mathrm{~m} \)
(c) \( 25 \mathrm{~cm} \)
(d) \( 50 \mathrm{~cm} \)
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