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A battery of $emf E_{0} = 6 V$ is connected across a $2 m$ long uniform wire having resistance $4 Ω / m$ . The cells of small $emf ε_{1} = 2 V and ε_{2} = 3 V$ having internal resistance $2 Ω & 1 Ω$ respectively are connected as shown in the figure. The null point will be obtained at

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$0.50 m$

$\frac{1}{5} m$

$0.25 m$

none of these

answer is D.

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Detailed Solution

Effective $emf$ of two cells in parallel

$ε = \frac{ε_{2} r_{1} - ε_{1} r_{2}}{r_{1} + r_{2}} = \frac{3 \times 2 - 2 \times 1}{2 + 1} = \frac{4}{3} V$

$X$ terminal of the connection is positive. For neutral point, positive terminal of $ε_{0}$ must be connected to $X$ .

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