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  4. A 10m long potentiometer wire has a resistance of 20 ohm . It is connected in series with a battery of emf 3 V and a resistance of 10 Ω . The internal resistance of cell is negligible. If the length can be read accurately up to 1 mm , the potentiometer can read voltage with an accuracy of (k/10) (in milli volt). Then the value of k is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-7ra07jbdjhsj7lfb.jpg />

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Q. A $10m$ long potentiometer wire has a resistance of $20\, ohm$ . It is connected in series with a battery of emf $3\,V$ and a resistance of $10\,\Omega$ . The internal resistance of cell is negligible. If the length can be read accurately up to $1\,mm$ , the potentiometer can read voltage with an accuracy of $\frac{k}{10}$ (in milli volt). Then the value of $k$ is
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NTA AbhyasNTA Abhyas 2022

Solution:

Current in wire $=\frac{3}{30}=0.1A$
$V=IR=2\,V$
maximum voltage can read $=2\,V$
$\lambda =\frac{V}{l}=\frac{2}{10 \times 10^{3}}=0.2\,m\,Vmm^{- 1}$
least account of scale $=1\,mm$
accuracy $=0.2\,mV$