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For the arrangement of the potentiometer shown in the figure, the balance point is obtained at $a$ distance $75\,cm $ from $A$ when the key $k$ is open. The second balance point is obtained at $60\, cm$ from $A$ when the key $k$ is closed. Find the internal resistance (in $ \Omega$) of the battery $E_1$.
The circuit shown in the figure consists of a battery of $emf$ $\varepsilon = 10 \,V$ ; a capacitor of capacitance $C = 1.0$ $ \mu F$ and three resistor of values $R_1 = 2$ $\Omega$ , $R_2 = 2$ $\Omega$ and $R_3 = 1$ $\Omega$ . Initially the capacitor is completely uncharged and the switch $S$ is open. The switch $S$ is closed at $t = 0.$
A current of $2\,A$ flows through a wire of crosssectional area $25.0\,mm ^2$. The number of free electrons in a cubic meter are $2.0 \times 10^{28}$. The drift velocity of the electrons is $...............\times 10^{-6}\,ms ^{-1}$ (given, charge on electron $=1.6 \times 10^{-19}\,C$ )
A resistance of $2 \Omega$ is comnected across one gap of a metre-bridge (the length of the wire is $100 \mathrm{~cm}$ ) and an unknown resistance, greater than $2 \Omega$, is connected across the other gap. When these resistance are interchanged, the balance point shifts by $20 \mathrm{~cm}$. Neglecting any corrections, the unknown resistance is