During an experiment with a meter bridge

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During an experiment with a meter bridge

Question :- During an experiment with a meter bridge, the galvanometer shows a null point when the jockey is pressed at 40.0 cm using a standard resistance of $90 Ω$ . The least count of the scale used in the meter bridge is 1mm. The unknown resistance is –

(1) 60 ± 0.15 Ω (2) 135 ± 0.56 Ω

(3) 60 ± 0.25 Ω (4) 135 ± 0.23 Ω

Solution :-

R is given by,

$\displaystyle R=90\times \frac{{{L}_{1}}}{{{L}_{2}}}=90\times \frac{40}{60}=60\Omega$

Now error in measurement of R is given by,

$\displaystyle \frac{dR}{R}=\frac{d{{L}_{1}}}{{{L}_{1}}}+\frac{d{{L}_{2}}}{{{L}_{2}}}$

$\displaystyle \Rightarrow dR=\left( \frac{d{{L}_{1}}}{{{L}_{1}}}+\frac{d{{L}_{2}}}{{{L}_{2}}} \right)\times R$

$\displaystyle \therefore dR=\left( \frac{0.1}{40}+\frac{0.1}{60} \right)\times 60=0.25\Omega$

Hence,

R = 60 ± 0.25 Ω

So correct option is (3).

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