A resistance of $2 \Omega$ is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than $2 \Omega$, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Current Electricity

A resistance of

2Ω

is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than

2Ω

, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

(A) $3Ω$ ✓ Correct
(B) $4Ω$
(C) $5Ω$
(D) $6Ω$

Answer: (A)

Solution

Let the unknown resistance be

x

and the initial balance point be at length

ℓ

from the

2Ω

side. By the metre-bridge principle:

\frac{2}{x} = \frac{ℓ}{100 - ℓ}

When the resistances are interchanged, the balance point shifts by 20 cm, so:

\frac{x}{2} = \frac{ℓ + 20}{80 - ℓ}

From the first equation:

2 (100 - ℓ) = x ℓ

From the second equation:

x (80 - ℓ) = 2 (ℓ + 20)

Solving these two equations simultaneously gives

x = 3Ω

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Single correct option

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JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Current Electricity

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