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Potential Energy

In the circui...

Question

In the circuit shown in figure. For what ratio $\frac{R_{2}}{R_{4}}$ current through $R_{3}$ will be zero ?

A

1 : 1

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B

1 : 2

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C

1 : 3

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D

2 : 3

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Solution

The correct option is D $2 : 3$
Since no current is flowing through $R_{3}$ , the potential drop across the branch is only due to the battery in the branch, i.e. of $15 V$ .
Potentials at the junctions are as marked in the figure above.
Current through $R_{4} = \frac{0 - (- 15)}{R_{4}} = \frac{15}{R_{4}}$
This current goes through $R_{2}$ .
But current in $R_{2} = \frac{- 5 - (- 15)}{R_{2}} = \frac{10}{R_{2}}$
$⟹ \frac{15}{R_{4}} = \frac{10}{R_{2}}$

$⟹ \frac{R_{2}}{R_{4}} = \frac{2}{3}$ .

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