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The diagram shows a modified meter bridge, which is used for measuring two unknown resistances at the same time. When only the first galvanometer is used, for obtaining the balance point, it is found at point C. Now the first galvanometer is removed and the second galvanometer is used, which gives balance point at D. Using the details given in the diagram, find out the value of $R_{1} a n d R_{2} .$

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$R_{1} = 5 R / 3$

$R_{2} = 4 R / 3$

$R_{1} = 4 R / 3$

$R_{2} = 5 R / 3$

answer is A, B.

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Detailed Solution

$\frac{R}{(R_{1} + R_{2})} = \frac{L / 4}{3 L / 4}$

$3 R = (R_{1} + R_{2})$

$\frac{R_{1} + R_{2}}{R} = \frac{2 / 3}{1 / 3}$

$3 R = R_{2} + R_{1}$

$R = 2 R_{2} - R_{1}$

$4 R = 3 R_{2}$

$R_{1} = \frac{5 R}{3}$

$R_{2} = \frac{4 R}{3}$

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