The power dissipated in the circuit shown in the figure is $30\, Watts$. The value of $R$ is ............. $\Omega$

When two identical batteries of internal resistance $1 \Omega$ each are connected in series across a resistor $\mathrm{R}$, the rate of heat produced in $R$ is $J_1$. When the same batteries are connected in parallel across $R$, the rate is $\mathrm{J}_2$. If $\mathrm{J}_1=2.25 \mathrm{~J}_2$ then the value of $\mathrm{R}$ in $\Omega$ is

On giving $220\,V$ to a resistor the power dissipated is $40\,W$ then value of resistance is ............... $\Omega$

Two electric bulbs whose resistances are in the ratio of $1 : 2$ are connected in parallel to a constant voltage source. The powers dissipated in them have the ratio

An electric fan and a heater are marked as $100\, watt$, $220\, volt$ and $1000\, watt$, $220\, volt$ respectively. The resistance of the heater is

$A$ constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is doubled if