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JEE Main 2020 (9 Jan, Shift 2) · Wheatstone Bridge & Metre Bridge

Wheatstone Bridge & Metre Bridge question from JEE Main 2020 (9 Jan, Shift 2)

Q64JEE Main 2020 · 9 JAN · SHIFT 2Medium

Wheatstone Bridge & Metre Bridge

In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is found that balancing length is $l$ = 25 cm. If R is replaced by a wire of half length and half diameter that of R of same material, then the balancing distance $l'$ (in cm) will now be________.

Numerical answer type. Work it out, then open the answer.

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Answer: 40

$\dfrac{R}{S} = \dfrac{25}{75} = \dfrac{1}{3}$ .
$R \propto \dfrac{L}{d^2}$ : half length and half diameter give $R' = \dfrac{1/2}{1/4}R = 2R$ .
$\dfrac{R'}{S} = \dfrac{2}{3} = \dfrac{l'}{100-l'} \Rightarrow l' = 40\text{ cm}$ .
$l' = 40\text{ cm}$ .

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