$A$ potentiometer has a uniform potential gradient across it. Two cells connected in series $(i)$ to support each other and $(ii)$ to oppose each other are balanced over $6 \ m$ and $2 \ m$ respectively on the potentiometer wire. The ratio of the $e.m.f.$s of the cells is:

$A$ $2.5 \ V$ battery is connected to a potentiometer wire. $A$ cell of e.m.f. $1.08 \ V$ is balanced by the voltage drop across $2.16 \ m$ of wire. The length of the potentiometer wire is (in $m$)

$A$ cell can be balanced against $110 \ cm$ and $100 \ cm$ of potentiometer wire,respectively with and without being short-circuited through a resistance of $10 \ \Omega$. Its internal resistance is

$A$ $2\,V$ battery,a $15\,\Omega$ resistor,and a potentiometer of $100\,cm$ length are all connected in series. If the resistance of the potentiometer wire is $5\,\Omega$,then the potential gradient of the potentiometer wire is ............... $V/cm$.

$A$ potentiometer wire,$10 \, m$ long,has a resistance of $40 \, \Omega$. It is connected in series with a resistance box and a $2 \, V$ storage cell. If the potential gradient along the wire is $0.1 \, mV/cm$,the resistance unplugged in the box is .............. $\Omega$.

$A$ potentiometer wire of length $100 \, cm$ has a resistance of $10 \, \Omega$. It is connected in series with a resistance $R$ and a cell of $emf$ $2 \, V$ and of negligible internal resistance. $A$ source of $emf$ $10 \, mV$ is balanced against a length of $40 \, cm$ of the potentiometer wire. What is the value of external resistance $R$?