Four resistances 3 Ω, 6 Ω, R and 4 Ω are connected in the form of quadrilateral in order. A battery is connected between two diagonally opposite corners with key closed. A galvanometer connected between the two remaining diagonally opposite points shows no deflection. The value of R would be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 8 Ω
No deflection means the Wheatstone bridge is balanced. Take the corners in order as A, B, C, D, with AB = 3 Ω, BC = 6 Ω, CD = R and DA = 4 Ω, the battery across A and C and the galvanometer across B and D.
Balance needs the same potential at B and D, so the two arms meeting at A must be in the same ratio as the two arms meeting at C:
\( \displaystyle \frac{AB}{BC} = \frac{AD}{DC} \)
\( \displaystyle \frac{3\,\Omega}{6\,\Omega} = \frac{4\,\Omega}{R} \)
\( \displaystyle R = 8\,\Omega \)
Putting the battery across B and D instead gives \( \frac{3}{4} = \frac{6}{R} \), the same result.