Physics · Kirchhoff's laws and their applications, Wheatstone bridge, Metre Bridge
A resistance of is connected across one gap of a metrebridge ( the length of the
A resistance of \( 2 \Omega \) is connected across one gap of a metrebridge ( the length of the wire is \( 100 \mathrm{cm} \) ) and an unknown resistance, greater than \( 2 \Omega, \) is connected across the other gap. When these resistance's are interchanged, the balance point shifts by \( 20 \mathrm{cm} \) Neglecting any corrections, the unknown resistance is:
- A. \( 3 \Omega \)
- B. \( 4 \Omega \)
- C. 5 \Omega \)
- D. \( 6 \Omega \)
Step-by-step solution
Let unknown resistance be X (>2Ω). Initially, with X in left gap and 2Ω in right gap, balance length l1 from left end satisfies X/2 = l1/(100-l1) => l1 = 100X/(X+2). After interchanging, with X in right gap and 2Ω in left gap, balance length l2 satisfies 2/X = l2/(100-l2) => l2 = 200/(X+2). The shift is 20 cm, and since X>2, l1 > l2, so l1 - l2 = 20. Substituting gives (100X-200)/(X+2)=20 => 100(X-2)=20(X+2) => 5(X-2)=X+2 => 4X=12 => X=3Ω.
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