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NEET2026PhysicsChapterActual

In the given circuit, the galvanometer G shows zero deflection. The resistance in arm AB is 8 , , the resistance in arm BC is 12 , , and the resistance in arm CD is 24 , . The arm AD consists of an unknown resistance R connected in series with a 6 , resistor. What is the value of the unknown resistance R ?

Options

  1. A16 ,
  2. B22 ,
  3. C30 ,
  4. D10 ,

Correct answer

D. 10 ,

Step-by-step solution

The given circuit is a Wheatstone bridge. Since the galvanometer shows zero deflection, the Wheatstone bridge is in a balanced condition. For a balanced Wheatstone bridge, the ratio of resistances in the adjacent arms is equal: R_ AB R_ BC = R_ AD R_ CD From the given circuit diagram: R_ AB = 8 , R_ BC = 12 , R_ CD = 24 , The resistance in arm AD is the series combination of R and 6 , : R_ AD = R + 6 Substituting these values into the balanced bridge condition: 8 12 = R + 6 24 Simplifying the equation: 2 3 = R + 6

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