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Two coils require $20$ minutes and $60$ minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be________ $min$
$A$ battery of $\mathrm{emf}$ $E_0 = 12\, V$ is connected across a $4\,m$ long uniform wire having resistance $4\,\Omega /m$. The cells of small $\mathrm{emfs}$ $\varepsilon_1 = 2\,V$ and $\varepsilon_2 = 4\,V$ having internal resistance $2\Omega$ and $6\Omega$ respectively, are connected as shown in the figure. If galvanometer shows no deflection at the point $N$, the distance of point $N$ from the point $A$ is equal to
A piece of wire is cut into four equal parts and the pieces are bundled together side by side to form a thicker wire. Compared with that of the original wire, the resistance of the bundle is ..........
Figure shows a part of an electric circuit. The potentials at points $a , b$ and $c$ are $30\,V , 12\,V$ and $2\,V$ respectively. The current through the $20 \Omega$ resistor will be $........\,A$
A uniform heating wire of resistance $36\, \Omega$ is connected across a potential difference of $240\, {V}$ The wire is then cut into half and potential difference of $240\, {V}$ is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be $1: {x}$, where ${x}$ is........... .
The Kirchhooff's first law $\left(\sum i=0\right)$ and second law ( $\left.\sum i R=\sum E\right)$, where the symbols have their usual meanings, are respectively based on