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A potentiometer wire is $100\,\, cm$ long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at $50\,\, cm$ and $10\,\, cm$ from the positive end of the wire in the two cases. The ratio of emf's is
In the given circuit diagram, the currents, ${I_1} = - \,0.3\,A,\,{I_4} = 0.8\,A$ and ${I_5} = 0.4\,A,$ are flowing as shown. The currents $I_2,\,I_3$ and $I_6,$ respectively are
The resistive network shown below is connected to a $D.C.$ source of $16\, V$. The power consumed by the network is $4\, Watt$. The value of $R$ is ............. $\Omega$
In an electrolyte $3.2 \times {10^{18}}$ bivalent positive ions drift to the right per second while $3.6 \times {10^{18}}$ monovalent negative ions drift to the left per second. Then the current is
In the given figure, battery $E $ is balanced on $55\, cm$ length of potentiometer wire but when a resistance of $10 \,\Omega$ is connected in parallel with the battery then it balances on $50\, cm$ length of the potentiometer wire then internal resistance $r$ of the battery is ............. $\Omega $
Three $60\, W$ light bulbs are mistakenly wired in series and connected to a $120\,V$ power supply. Assume the light bulbs are rated for single connection to $120\,V$. With the mistaken connection, the power dissipated by each bulb is: .................. $W$