Two ideal batteries of emf $V _1$ and $V _2$ and three resistances $R _1, R _2$ and $R _3$ are connected as shown in the figure.
The current in resistance $R _2$ would be zero if
$(A)$ $V_1=V_2$ and $R_1=R_2=R_3$
$(B)$ $V_1=V_2$ and $R_1=2 R_2=R_3$
$(C)$ $V_1=2 V_2$ and $2 R_1=2 R_2=R_3$
$(D)$ $2 V _1= V _2$ and $2 R _1= R _2= R _3$
IIT 2014, Medium
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Potential of Junction $O$
$V_0=\frac{\frac{V_1}{R_1}+0-\frac{V_2}{R_3}}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}}$
Current through $R_2$ will be zero if $R _2$
$V_0=0 \Rightarrow \frac{V_1}{V_2}=\frac{R_1}{R_3}$
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