In the circuit shown the cells are ideal and of equal emfs, the capacitance of the capacitor is $C$ and the resistance of the resistor is $R. X$ is first joined to $Y$ and then to $Z$. After a long time, the total heat produced in the resistor will be
equal to the energy finally stored in the capacitor
half of the energy finally stored in the capacitor
twice the energy finally stored in the capacitor
$4$ times the energy finally stored in the capacitor
Two wires have resistance of $2$ $\Omega$ and $4$ $\Omega$ connected to same voltage, ratio of heat dissipated at resistance is
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
An electric bulb of $500 \,watt$ at $100\, volt$ is used in a circuit having a $200\, {V}$ supply. Calculate the resistance ${R}$ to be connected in series with the bulb so that the power delivered by the bulb is $500\, {W}$. (in $\Omega$)
A $50 \,W$ bulb connected in series with a heater coil is put to an $AC$ mains. Now the bulb is replaced by a $100 \,W$ bulb. The heater output will ...........
In a building there are $15$ bulbs of $45\; \mathrm{W}, 15$ bulbs of $100\; \mathrm{W}, 15$ small fans of $10 \;\mathrm{W}$ and $2$ heaters of $1 \;\mathrm{kW}$. The voltage of electric main is $220\; \mathrm{V}$. The minimum fuse capacity (rated value) of the building will be: .......... $A$