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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 $t = 0.$
The two ends of a uniform conductor are joined to a cell of $e.m.f.$ $E$ and some internal resistance. Starting from the midpoint $P$ of the conductor, we move in the direction of current and return to $P$. The potential $V$ at every point on the path is plotted against the distance covered $(x)$. Which of the following graphs best represents the resulting curve
A current of $10\, A$ exists in a wire of crosssectional area of $5\, mm ^{2}$ with a drift velocity of $2 \times 10^{-3}\, ms ^{-1}$. The number of free electrons in each cubic meter of the wire is ..........
By error, a student places moving-coil voltmeter $V$ (nearly ideal) in series with the resistance in a circuit in order to read the current, as shown. The voltmeter reading will be ............ $V$
In the Wheatstone's bridge shown, $P = 2\,\Omega ,$ $Q = 3\,\Omega ,$ $R = 6\,\Omega $ and $S = 8\,\Omega $. In order to obtain balance, shunt resistance across '$S$' must be .............. $\Omega$