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 give 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

Answer: (C)

Let current flowing in the wire is $i$.
$\therefore i=\left(\frac{4}{R+5}\right)A$
If resistance of 10 m 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
$5\times 10^{-3}=\left(\frac{4}{R+5}\right).\left(0.5\right)$
$\therefore \frac{4}{R+5}=10^{-2}R+5=400\Omega$
$\therefore R=395\Omega$