Question

A potentiometer wire of length $100cm$has a resistance of $10\Omega$. It is connected in series with an external resistance and a cell of emf $2V$ and negligible internal resistance. A source of emf $10mV$ is balanced against a length of $40cm$ of the potentiometer wire.Then the value of external resistance is

• A. $800\Omega$
• B. $790\Omega$
• C. $825\Omega$
• D. $745\Omega$

Answer 1

The correct option is B

$790\Omega$

As shown in figure, if $R$ is the unknown resistance, current in the circuit

$I=\frac{V}{(r+R)}=\frac{2}{(10+R)}$

Now, as $100cm$ wire has resistance $10\Omega$, the resistance of $40cm$ wire will be

$40\times \left(\frac{10}{100}\right)=4\Omega$.

Potential drop across 40 cm wire will be
$V=I\times 4$

But $V=10\text{mV (given)}$

And $V=\frac{2}{(10+R)}\times 4\Rightarrow R=790\Omega$