Q

# I have a doubt, kindly clarify. - Current Electricity - NEET-3

A potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery used across the potentiometer wire , has an emf of 2.0V and a negligible internal resistance. The potentiometer wire itself is 4m long, when the resistance R, connected across the given cell, has value of

(i) infinity              (ii) 9.5$\Omega$

The balancing lengths', on the potentiometer  wire are found to be 3 m and 2.85m, respectivily. The value of internal resistance of the cell is

• Option 1)

0.25$\Omega$

• Option 2)

0.95$\Omega$

• Option 3)

0.5$\Omega$

• Option 4)

0.75$\Omega$

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Determine the internal resistance -

$r=(\frac{l_{1}-l_{2}}{l_{2}})R$

$r=(\frac{E}{V}-1)R$

$\frac{E}{V}=\frac{l_{1}}{l_{2}}$

- wherein

potential across wire =2V

$\therefore$ $potential/length =\frac{2}{4}=0.5\: V/m$

$(\phi )$

${e}'=\phi l_{1} ------(1)$

$v=\phi\: l_{2}--------(2)$

=> ${e}'=l(r+R)$

$r=R(\frac{l_{1}}{l_{2}}-1) = 9.5 (\frac{.3}{2.85} -1)$

r=$0.5\Omega$

Option 1)

0.25$\Omega$

This is incorrect option

Option 2)

0.95$\Omega$

This is incorrect option

Option 3)

0.5$\Omega$

This is correct option

Option 4)

0.75$\Omega$

This is incorrect option

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