Q. Potentiometer wire of length 1m is connected in series with 490$\Omega$resistance and 2V battery. If 0.2m V$cm^{- 1}$is the potential gradient, then resistance of the potentiometer wire is
A) 4.9$\Omega$
B) 7.9$\Omega$
C) 5.9$\Omega$
D) 6.9$\Omega$
Explanation
(a) When a constant current is passed through a wire of uniform cross-section, the potential difference across any portion of the wire is directly proportional to the length of that portion.
Potential gradient=$0.2\ mVcm^{- 1}$
∴ Potential difference across potentiometer wire
=0.02 × 1= 0.02V
Total resistance $= r + R = 490 + R$
$\therefore\ \ \ \ \ \frac{V_{1}}{V_{2}} = \frac{R_{1}}{R_{2}}$
$\Longrightarrow \frac{0.02}{2} = \frac{R}{490 + R}$
$\Longrightarrow R = 4.9\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.