$A$ current $I$ flows through a uniform wire of diameter $d$ when the mean electron drift velocity is $V$. The same current will flow through a wire of diameter $d/2$ made of the same material if the mean drift velocity of the electron is :
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It is preferable to measure the $e.m.f.$ of a cell by potentiometer than by a voltmeter because of the following possible reasons.
$(i)$ In case of potentiometer, no current flows through the cell.
$(ii)$ The length of the potentiometer allows greater precision.
$(iii)$ Measurement by the potentiometer is quicker.
$(iv)$ The sensitivity of the galvanometer, when using a potentiometer is not relevant.
Which of these reasons are correct?
A wire of length ' $r$ ' and resistance $100 \Omega$ is divided into $10$ equal parts. The first $5$ parts are connected in series while the next $5$ parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:
Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:
The resistors of resistances $2$ $\Omega$, $4$ $\Omega$ and $8$ $\Omega$ are connected in parallel, then the equivalent resistance of the combination will be
A torch bulb rated as $4.5\, W$, $1.5\, V$ is connected as shown in the figure. The $e.m.f.$ of the cell needed to make the bulb glow at full intensity is ................ $V$