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

Wheat stone bridge is balanced. Find ratio of electric power dissipated in $(P + Q)$ to $(R + S)$

Two heating coils, one of fine wire and the other of thick wire of the same material and of the same length are connected in series and in parallel. Which of the following statement is correct

A heater of $220\, V$ heats a volume of water in $5\,\min$ time. A heater of $110\, V$ heats the same volume of water in ............... $min$

Six similar bulbs are connected as shown in the figure with a $DC$ source of $emf\; E$, and zero internal resistance. The ratio of power consumption by the bulbs when $(i)$ all are glowing and $(ii)$ in the situation when two from section $A$ and one from section $B$ are glowing, will be

Two bulbs are in parallel and they together consume $48\, W$ from a battery of $6\, V$. The resistance of each bulb is ............ $\Omega$