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In the network shown, when the terminals of a 10 V cell are connected to A and B, and a galvanometer having coil resistance $100 Ω$ is connected between C and D, no deflection is registered in the galvanometer. If the same cell is connected between C and D and the same galvanometer is connected between A and B, current flowing through the cell is

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$\frac{17}{9} A$

$\frac{24}{11} A$

$\frac{15}{8} A$

$\frac{25}{9} A$

answer is D.

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Detailed Solution

In the first case, the network must be a balanced wheat stone bridge.

$∴ \frac{R}{6} = \frac{2}{4} \Rightarrow R = 3 Ω$

In the second case also the circuit is a balanced wheat stone bridge as $\frac{2}{3} = \frac{4}{6}$

$∴ R_{e} = \frac{(4 + 2) (6 + 3)}{(4 + 2) + (6 + 3)} Ω = \frac{18}{5} Ω$

$∴ i = \frac{10}{(18 / 5)} A = \frac{25}{9} A$

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