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 ...........

A torch bulb rated as $4.5\, W, 1.5\, V$ is connected as shown in the figure. The $e.m.f.$ of the cell needed to make the bulb glow at full intensity is ............. $V$

The electric bulbs have tungsten filaments of same length. If one of them gives $60 \,watt$ and other $100\, watt$, then

An expression for rate of heat generated, if a current of $I$ ampere flows through a resistance of $R$ $\Omega$, is

Two wires have resistance of $2$ $\Omega$ and $4$ $\Omega$ connected to same voltage, ratio of heat dissipated at resistance is

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, $100 \mathrm{~W}, 60 \mathrm{~W}$ and $40 \mathrm{~W}$ bulbs have filament resistances $\mathrm{R}_{100}, \mathrm{R}_{60}$ and $\mathrm{R}_{40}$, respectively, the relation between these resistances is