Question

An ideal battery of $4V$ and resistance $R$ are connected in series in the primary circuit of a potentiometer of length $1m$ and resistance $5\Omega$. The value of $R$, to given a potential difference of $5mV$across $10cm$ of potentiometer wire is:

• A. $490\Omega$
• B. $480\Omega$
• C. $395\Omega$
• D. $495\Omega$

Answer 1

The correct option is C $395\Omega$

Let current flowing in the wire is i.
$\therefore i=\left(\frac{4}{R+5}\right)A$
If resistance of $10m$ length of wire is $x$
then $x=0.5\Omega =5\times \frac{0.1}{1}\Omega$
$\therefore \Delta V=P.d$ on wire $=i.x$
$5\times {10}^{-3}=\left(\frac{4}{R+5}\right)\left(0.5\right)$
$\therefore \frac{4}{R+5}={10}^{-2}$
$\therefore R=395\Omega$