$A$ potentiometer wire of length $1 \, m$ is connected in series with a $490 \, \Omega$ resistance and a $2 \, V$ battery. If the potential gradient is $0.2 \, mV/cm$,then the resistance of the potentiometer wire is ................ $\Omega$. (in $.9$)

$A$ $2 \, V$ battery, a $990 \, \Omega$ resistor, and a potentiometer of $2 \, m$ length are connected in series. If the resistance of the potentiometer wire is $10 \, \Omega$, then the potential gradient of the potentiometer wire is: (in $V m^{-1}$)

The length of a potentiometer wire is $1200 \; cm$ and it carries a current of $60 \; mA$. For a cell of $emf \; 5 \; V$ and internal resistance of $20 \; \Omega$,the null point on it is found to be at $1000 \; cm$. The resistance of the whole wire is .............. $\Omega$.

The current in the primary circuit of a potentiometer is $0.2 \, A$. The specific resistance and cross-section of the potentiometer wire are $4 \times 10^{-7} \, \Omega \cdot m$ and $8 \times 10^{-7} \, m^2$ respectively. The potential gradient will be equal to .............. $V/m$.

With the help of a potentiometer,we can determine the value of the emf of a given cell. The sensitivity of the potentiometer is:
$(A)$ directly proportional to the length of the potentiometer wire
$(B)$ directly proportional to the potential gradient of the wire
$(C)$ inversely proportional to the potential gradient of the wire
$(D)$ inversely proportional to the length of the potentiometer wire
Choose the correct option for the above statements:

$A$ potentiometer wire of length $300\,cm$ is connected in series with a resistance $780\,\Omega$ and a standard cell of emf $4\,V$. $A$ constant current flows through the potentiometer wire. The length of the null point for a cell of emf $20\,mV$ is found to be $60\,cm$. The resistance of the potentiometer wire is ... $\Omega$.