JEE Advanced · Physics · 19. Current Electricity

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

Verified Solution

Answer & Solution

Correct Answer

(A) $V_{1} = V_{2}$ and $R_{1} = R_{2} = R_{3}$

Step-by-step Solution

Detailed explanation

In order that the current is zero, the potential drop on

R_{2}

due to

V_{1}

must be nullified by that due to

V_{2}

.
Accordingly,

V_{1} = \frac{R_{1} (V_{1} + V_{2})}{R_{1} + R_{3}} \Rightarrow V_{1} R_{3} = V_{2} R_{1}

V_{2} = \frac{R_{3} (V_{1} + V_{2})}{R_{1} + R_{3}} \Rightarrow V_{2} R_{1} = V_{2} R_{3}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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

Step-by-step Solution

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