In a potentiometer wire experiment the $\mathrm{emf}$ of a battery in the primary circuit is $20\,V$ and its internal resistance is $5\,\Omega$ . There is a resistance box in series with the battery and the potentiometer wire, whose resistance can be varied from $120\,\Omega$ to $170\,\Omega$ . Resistance of the potentiometer wire is $75\,\Omega$ . The following potential differences can be measured using this potentiometer.
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First, a set of ${n}$ equal resistors of $10\; \Omega$ each are connected in series to a battery of emf $20\; {V}$ and internal resistance $10\; \Omega .$ A current $I$ is observed to flow. Then, the $n$ resistors are connected in parallel to the same battery. It is observed that the current is increased $20$ times, then the value of $n$ is .... .
Two indentical electric lamps marked $500\, W, \,\,220\, V$ are connected in series and then joined to a $110\, V$ line. The power consumed by each lamp is
ln the circuit in the figure, if no current flows through the galvanometer when the key $K$ is closed, the bridge is balanced. The balancing condition for bridge is
A metal wire of resistance $3\,\Omega $ is elongated to make a uniform wire of double its previous length. The new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle $60^o$ at the centre, the equivalent resistance between these two points will be
Consider a $72\, cm$ long wire $AB$ as shown in the figure. The galvanometer jockey is placed at $P$ on $A B$ at a distance $x cm$ from $A$. The galvanometer shows zero deflection.
The value of $x,$ to the nearest integer, is ..... $cm$
The resistance of a coil is $4.2\, \Omega$ at $100\,^o C$ and the temperature coefficient of resistance of its material is $ 0.004\,^o C$. Its resistance at $0\,^o C$ is ............. $\Omega$
$12$ cells each having same $emf$ are connected in series with some cells wrongly connected. The arrangement is connected in series with an ammeter and two cells which are in series. Current is $3 \,A$ when cells and battery aid each other and is $2\, A$ when cells and battery oppose each other. The number of cells wrongly connected is
Resistance of the wire is measured as $2\,\Omega$ and $3\,\Omega$ at $10^{\circ}C$ and $30^{\circ}C$ respectively. Temperature cocoefficient of resistance of the material of the wire is............$^{\circ}C ^{-1}$