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The resistance of a wire is $R$. It is bent at the middle by $180^o$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is
$AB$ is a potentiometer wire of length $100\, cm$ and its resistance is $10 \,\Omega$. It is connected in series with a resistance $R = 40 \,\Omega$ and a battery of $e.m.f.$ $2 \,V$ and negligible internal resistance. If a source of unknown $e.m.f.$ $E$ is balanced by $40\, cm$ length of the potentiometer wire, the value of $E$ is ................. $V$
A thick wire is stretched so that its length become two times. Assuming that there is no change in its density, then what is the ratio of change in resistance of wire to the initial resistance of wire