In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation (dR)/(d) of its resistance R with length is (dR)/(d) ∝ (1)/(√()). Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP? (a) 0.3 m (b) 0.25 m (c) 0.35 m (d) 0.2 m

Answer: (b). R() ∝ ∫₀ (d)/(√()) ∝ √(). Equal resistances in the gaps, so wire resistance AP = PB: √() = √(1) - √(). √() = 1/2 ⇒ = 0.25 m. So the answer is (b) 0.25 m.

In a meter bridge, the wire of length 1 m has a non-uniform… | JEE Main 2019 (12 Jan, Shift 1)

Q72JEE Main 2019 · 12 JAN · SHIFT 1Difficult

Wheatstone Bridge & Metre Bridge

In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation $\frac{dR}{d\ell}$ of its resistance R with length $\ell$ is $\frac{dR}{d\ell} \propto \frac{1}{\sqrt{\ell}}$ . Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP?

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Answer: (b)

$R(\ell) \propto \int_0^{\ell} \dfrac{d\ell}{\sqrt{\ell}} \propto \sqrt{\ell}$ .
Equal resistances in the gaps, so wire resistance AP = PB: $\sqrt{\ell} = \sqrt{1} - \sqrt{\ell}$ .
$\sqrt{\ell} = \dfrac{1}{2} \Rightarrow \ell = 0.25\text{ m}$ .
So the answer is (b) 0.25 m.

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Wheatstone Bridge & Metre Bridge question from JEE Main 2019 (12 Jan, Shift 1)

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