Question

In a metre bridge experiment , resistance box with 2 Ω is connected in the left gap and the unknown resistance S in the right gap. If the balancing length be 40 cm, value of S will be *

(a) 2 Ω

(b) 3 Ω

(c) 4 Ω

(d) 5 Ω

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Answer 1

Given:

In a metre bridge experiment , resistance box with 2 Ω is connected in the left gap and the unknown resistance S in the right gap. Balancing length is at 40 cm.

To find:

Value of "S".

Calculation:

A metre - bridge essentially works on the principles of a balanced WHEATSTONE BRIDGE where the adjacent resistances are in ratio.

$\therefore \: \dfrac{2}{S} = \dfrac{l}{100 - l}$

$\implies\: \dfrac{2}{S} = \dfrac{40}{100 - 40}$

$\implies\: \dfrac{2}{S} = \dfrac{40}{60}$

$\implies\: \dfrac{2}{S} = \dfrac{2}{3}$

$\implies\: \dfrac{1}{S} = \dfrac{1}{3}$

$\implies\: S = 3 \: \Omega$

So, final answer is:

$\boxed{ \bold{\: S = 3 \: \Omega }}$