Question

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

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

Answer 1

Answer: (C)

$395\Omega$

Answer 2

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
$5 \times10^{-3} = \left(\frac{4}{R +5}\right).\left(0.5\right)$
$\therefore \frac{4}{R+5} = 10^{-2} R +5 = 400 \Omega$
$\therefore R = 395 \Omega$