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A copper wire of length $10\,m$ and radius $\left(10^{-2} / \sqrt{\pi}\right) m$ has electrical resistance of $10 \,\Omega$. The current density in the wire for an electric field strength of $10( V / m )$ is :
Circuit for the measurement of resistance by potentiometer is shown. The galvanometer is first connected at point $A$ and zero deflection is observed at length $P J = 10\ cm$ . In second case it is connected at point $C$ and zero deflection is observed at a length $30\ cm$ from $P$ . Then the unknown resistance $X$ is
A potentiometer wire of length $1\,m$ and resistance $10\,\Omega$ is connected in series with a cell of $emf$ $2\,V$ with internal resistance $1 \,\Omega$ and a resistance box including a resistance $R$. If potential difference between the ends of the wire is $1\, mV$, the value of $R$ is ............. $\Omega $
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 ................ $V$
By a cell a current of $0.9\, A$ flows through $2\, ohm$ resistor and $0.3\,A$ through $7\, ohm$ resistor. The internal resistance of the cell is ............ $\Omega$