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A potentiometer wire of length $L$ and a resistance $r$ are connected in series with a battery of e.m.f. $E_0$ and a resistance $r_1$. An unknown e.m.f. $E$ is balanced at a length $l$ of the potentiometer wire. The e.m.f. $E$ will be given by
The current in a wire varies with time according to relation $I = 4 + 2t$. The quantity of charge which has passed through a crosssectionn of the wire during the time $t = 2\, s$ to $t = 6\, s$ will be .............. $\mathrm{C}$
A $9\, V$ battery with internal resistance of $0.5\,\Omega $ is connected across an infinite network as shown in the figure. All ammeters $A_1 , A_2, A_3$ and voltmeter $V$ are ideal. Choose correct statement
In a region $10^{19}$ $\alpha -$ particels and $10^{19}$ protons per second move to the left, while $10^{19}$ electrons moves to the right per second. The current is
In the figure the potentiometer wire of length $l =100\, cm$ and resistance $9\Omega$ is joined to a cell of emf $E_1 = 10V$ and internal resistance $r_1 = 1\Omega $. Another cell of emf $E_2 = 5\, V$ and internal resistance $r_2 = 2 \Omega $ is connected as shown. The galvanometer $G$ will show no deflection when the length $AC$ is ............... $cm$
In the network shown in the figure, each of the resistance is equal to $2\,\Omega $. The resistance between the points $A$ and $B$ is .............. $\Omega$