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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

Options

  1. AV 1 = V 2 and R 1 = R 2 = R 3
  2. BV 1 = V 2 and R 1 = 2 R 2 = R 3
  3. CV 1 = 2 V 2 and 2 R 1 = 2 R 2 = R 3
  4. D2 V 1 = V 2 and 2 R 1 = R 2 = R 3

Correct answer

A. V 1 = V 2 and R 1 = R 2 = R 3

Step-by-step solution

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 = R 1 V 1 + V 2 R 1 + R 3 ⇒ V 1 R 3 = V 2 R 1 V 2 = R 3 V 1 + V 2 R 1 + R 3 ⇒ V 2 R 1 = V 2 R 3

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