Question

A 2V battery, a $990\Omega$ resistor and a potentiometer of 2m length, all are connected in series, the resistance of potentiometer wire is $10\Omega$, then the potential gradient of potentiometer wire is:

• A. 0.05 Vm
• B. 0.5 V/m
• C. 0.01 V/m
• D. 0.1 V/m

Answer 1

The correct option is C 0.01 V/m

$R_{eff}=R_{wire}+R_{resistor}$
$=10\Omega +990\Omega =1000\Omega$
'V' drop across wire
$V_w=I\times R_{wire}$
$V_w=\frac{V_{battery}}{R_{eff}}\times 10\Omega$
$V_w=\frac{2}{1000}\times 10=2\times {10}^{-2}volt$
Potential gradient $=\frac{V_w}{l}=\frac{2\times {10}^{-2}}{2}$
$\frac{V}{l}=0.01volt/metre$