Question

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

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

Answer 1

The correct option is A $395\Omega .$


Current flowing through the circuit $\left(I\right)$ is given by,

$I=\left(\frac{4}{R+5}\right)\text{A}$

Resistance of length $10\text{cm}$ of wire
$=5\times \frac{100}{100}=0.5\Omega$

According to question,

$5\times 10-3=\left(\frac{4}{R+5}\right).\left(0.5\right)$

$\therefore \frac{4}{R+5}={10}^{-2}\text{or}R+5=400\Omega$

$\therefore R=395\Omega$