Question

Potentiometer wire of length 1 m is connected in series with 490 $\Omega$ resistance and 2 V battery. If 0.2 mV/cm is the potential gradient, the resistance of the potentiometer wire is

• A. 4.9 $\Omega$
• B. 7.9 $\Omega$
• C. 5.9 $\Omega$
• D. 6.9 $\Omega$

Answer 1

The correct option is A 4.9 $\Omega$

Potential gradient, $k=0.2mV/cm=\frac{0.2\times {10}^{-3}}{{10}^{-2}}=0.02V/m$
Potential across potentiometer wire is $V_p=kl=0.02\times 1=0.02V$
If $R$ be the resistance of potentiometer wire, as per the condition of potnetiometer:
$0.02\times (R+490)=2R$
or $1.98\times R=9.8$
$\therefore R=4.9\Omega$