Two resistors of resistance $100\,\Omega$ and $200\,\Omega$ are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in $100\,\Omega$ to that in $200\,\Omega$ in a given time is:

For three resistors of different values connected in series,obtain the equation for equivalent resistance. From this,write the equation for $n$ resistors connected in series.

$A$ cube is formed with ten identical resistances $R$ (thick lines) and two shorting wires (dotted lines) along the arms $AC$ and $BD$ as shown in the figure below. The resistance between point $A$ and $B$ is ........... $\Omega$.

$A$ 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).

Three resistances of equal values $R$ are arranged in four different configurations as shown in the figure. The power dissipation in increasing order is:

In the given circuit,the equivalent resistance between $A$ and $B$ is ....... $\Omega$.