A $50\,V$ battery is connected across a $10\, ohm$ resistor. The current is $4.5\, amperes$. The internal resistance of the battery is ............. $ohm$
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Twelve wires each having resistance $2 \Omega$ are joined to form a cube. A battery of $6 \mathrm{~V}$ emf is joined across point $\mathrm{a}$ and $\mathrm{c}$. The voltage difference between $e$ and $f$ is.______.V.
When a current of $2\,A$ flows in a battery from negative to positive terminal, the potential difference across it is $12\,V$. If a current of $3\,A$ flows in the opposite direction potential difference across the terminals of the battery is $15\,V$, the emf of the battery is ............... $\mathrm{V}$
Two resistances ${R_1}$ and ${R_2}$ are made of different materials. The temperature coefficient of the material of ${R_1}$ is $\alpha $ and of the material of ${R_2}$ is $ - \beta $. The resistance of the series combination of ${R_1}$ and ${R_2}$ will not change with temperature, if ${R_1}/{R_2}$ equals