A uniform wire of resistance $R$ is uniformly compressed along its length, until its radius becomes $n$ times the original radius. Now resistance of the wire becomes
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The figure shows three circuits $I, II$ and $III$ which are connected to a $3\,V$ battery. If the powers dissipated by the configurations $I, II$ and $III$ are $P_1 , P_2$ and $P_3$ respectively, then
A $3\,^oC$ rise in temperature is observed in a conductor by passing a certain current. When the current is doubled, the rise in temperature will be ............. $^oC$
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 $t = 0.$
Two cells are connected in opposition as shown. Cell $\mathrm{E}_1$ is of $8 \mathrm{~V}$ emf and $2 \ \Omega$ internal resistance; the cell $E_2$ is of $2 \mathrm{~V}$ emf and $4\ \Omega$ internal resistance. The terminal potential difference of cell $\mathrm{E}_2$ is:
A potentiometer circuit shown in the figure is set up to measure $e.m.f.$ of a cell $E$. As the point $P$ moves from $X$ to $Y$ the galvanometer $G$ shows deflection always in one direction, but the deflection decreases continuously until $Y$ is reached. In order to obtain balance point between $X$ and $Y$ it is necessary to