Question

A potentiometer wire, $10 \,m$ long, has a resistance of $40\,\Omega$ . It is connected in series with a resistance box and a $2 \,V$ storage cell. If the potential gradient along the wire is $(0.1\, mV/cm)$, the resistance unplugged in the box is

• A. $260\,\Omega$
• B. $760\,\Omega$
• C. $960\,\Omega$
• D. $1060\,\Omega$

Answer 1

Answer: (B)

$760\,\Omega$

Answer 2

Potential gradient along wire
$=\frac{potential\text{ }difference\text{ }along\text{ }wire}{length\text{ }of\text{ }wire}$
$\therefore$ $0.1\times {{10}^{-3}}=\frac{I\times 40}{1000}V/cm$
Current in wire, $I=\frac{1}{400}A$
Or $I=\frac{E}{R+R}$
$\therefore$
$\frac{2}{40+R}=\frac{1}{400}$
Or $R=800-40$
$=760\,\Omega$