A resistance wire connected in the left gap of a metre bridge balances a 10 resistance in the right gap at a point which divides the bridge wire in the ratio 3 : 2. If the length of the resistance wire is 1.5 m, then the length of 1 of the resistance wi

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Solution

Q.
A resistance wire connected in the left gap of a metre bridge balances a 10 $Ω$ resistance in the right gap at a point which divides the bridge wire in the ratio 3 : 2. If the length of the resistance wire is 1.5 m, then the length of 1 $Ω$ of the resistance wire is [2020]

1 $1.0 \times 10^{- 2} m$

2 $1.0 \times 10^{- 1} m$

3 $1.5 \times 10^{- 1} m$

4 $1.5 \times 10^{- 2} m$

Ans.
(2)

Unknown is $X, R = 10$ $Ω$ .

Here, $\frac{l_{1}}{l_{2}} = \frac{3}{2}; \frac{X}{R} = \frac{l_{1}}{l_{2}}$

$\Rightarrow X = \frac{3}{2} \times 10 \Rightarrow X = 15 Ω$

Thus, 1.5 m length has resistance $15 Ω$ hence, length of $1 Ω$ of the resistance wire $= \frac{1.5}{15} = 0.1 m = 1.0 \times 10^{- 1} m$

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