The ratio of heat dissipated per second through the resistance $5 \Omega$ and $10 \Omega$ in the circuit given below is: :

A heating coil can heat the water of a vessel from $20\,^oC$ to $60\,^oC$ in $30$ minutes. Two such heating coils are put in series and then used to heat the same amount of water through the same temperature range. The time taken now will be ............ $min$ (neglecting thermal capacity of the coils)

How many calories of heat will be produced approximately in a $210\, watt$ electric bulb in $5$ minutes .............. $cal $

A resistance $R = 12\, \Omega$ is connected across a source of emf as shown in the figure . Its $emf$ changes with time as shown in the graph . What is the heat developed in the resistance in the first four seconds ? ............. $J$

If power in $3\,\Omega $ is $27\,W$ then what is the power in $2\,\Omega $  ................ $\mathrm{W}$

A $220 \; V , 50 \; Hz$ AC source is connected to a $25 \; V$, $5 \; W$ lamp and an additional resistance $R$ in series (as shown in figure) to run the lamp at its peak brightness, then the value of $R$ (in ohm) will be