Question

How much resistance is to be connected in series with the potentiometer wire to have a potential gradient of $0.05$ mV cm${}^{-1}$?

• A. $1990\Omega$
• B. $2000\Omega$
• C. $1995\Omega$
• D. $none$ $of$ $these$

Answer 1

Answer: (C)

$1995\Omega$

Here,$k=0.05$ mV cm${}^{-1}=5$ mV m${}^{-1}$
Let $R$ be the resistance is to be connected in series with the potentiometer wire, the potential of driver cell is
$V=I(R+5)$.................................................(1)
The current through the potentiometer wire is,
$I=\frac{kl}{r}=\frac{5\times {10}^{-3}\times 1}{5}={10}^{-3}A$
Hence, from(1)
$2=I(R+r)={10}^{-3}(R+5)$
$R=2000-5$
$R=1995\Omega$