In an experiment of a potentiometer for measuring the internal resistance of a primary cell,a balancing length $\ell$ is obtained on the potentiometer wire when the cell is in an open circuit. Now,the cell is short-circuited by a resistance $R$. If $R$ is equal to the internal resistance of the cell,the balancing length on the potentiometer wire will be:

$A$ thermocouple of negligible resistance produces an $e.m.f.$ of $40\,\mu V/^{\circ}C$ in the linear range of temperature. $A$ galvanometer of resistance $10\,\Omega$ whose sensitivity is $1\,\mu A/\text{div}$ is employed with the thermocouple. The smallest value of temperature difference that can be detected by the system will be (in $^{\circ}C$)

In a potentiometer experiment, the null point is obtained at a particular point for a cell on a potentiometer wire of length $L$. If the length of the potentiometer wire is increased without changing the cell or the driving source, the balancing length will:

In a potentiometer,when the cell in the secondary circuit is shunted with a $4 \ \Omega$ resistance,the balance is obtained at a length of $120 \ cm$ of the wire. Now,when the same cell is shunted with a $12 \ \Omega$ resistance,the balance point shifts to a length of $180 \ cm$. The internal resistance of the cell is . . . . . . $\Omega$.

In the experiment of calibration of a voltmeter,a standard cell of $e.m.f. = 1.1 \text{ V}$ is balanced against $440 \text{ cm}$ of a potentiometer wire. The potential difference across a resistance is found to balance against $220 \text{ cm}$ of the wire. The corresponding reading of the voltmeter is $0.5 \text{ V}$. The error in the reading of the voltmeter will be ................. $V$.

$A$ null point is found at $200\,cm$ in a potentiometer when the cell in the secondary circuit is shunted by $5\,\Omega$. When a resistance of $15\,\Omega$ is used for shunting,the null point moves to $300\,cm$. The internal resistance of the cell is $..............\,\Omega$.