Advanced 2014 | JEE 2014 | Discussion Page

Two ideal batteries of emf V₁ and V₂ and three resistance R₁, R₂ and R₃ are connected as shown in the figure. The current in resistance R₂ would be zero if

$V_{1}=V_{2}$ and

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

$V_{1}=V_{2}$ and

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

$V_{1}=2V_{2}$ and

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

$2V_{1}=V_{2}$ and

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

Answer:

Option A,B,D

Explanation:

Let us take $V_{P}=0$ .Then potentials acrosds $R_{1}$ , $R_{2}$ and $R_{3}$ are as shown in figure(ii)

In the same figure.

i₁ +i₂ =i₃

$\therefore$ $\frac{V_{1}-V_{0}}{R_{1}}+\frac{0-V_{0}}{R_{2}}=\frac{V_{0}-(-V_{2})}{R_{3}}$

Solving this equation we get,

$V_{0}=\frac{\frac{V_{1}}{R_{1}}+0-\frac{V_{2}}{R_{2}}}{\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}}$

Current througfh R₂ will be zero if

$V_{0}=0\Rightarrow\frac{V_{1}}{V_{2}}=\frac{R_{1}}{R_{2}}$

In options (a),(b), and (d) this reaction is satisfied

Discussion Forum

Answer:

Explanation: