Question

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 $2 R _{1}= R _{2}= R _{3}$

Answer 1

Answer: (D)

$2 V _{1}= V _{2}$ and $2 R _{1}= R _{2}= R _{3}$

Answer 2

$V _{1}=\frac{ R _{1}\left( V _{1}+ V _{2}\right)}{ R _{1}+ R _{3}}$ $\Rightarrow V _{1} R _{3}= V _{2} R _{1}$ $V _{2}=\frac{ R _{3}\left( V _{1}+ V _{2}\right)}{ R _{1}+ R _{3}}$ $\Rightarrow V _{2} R _{1}= V _{2} R _{3}$