Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage,the ratio of heat produced in the same time for parallel to series will be:

$A$ 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).

$3$ identical bulbs are connected in series and these together dissipate a power $P$. If now the bulbs are connected in parallel,then the power dissipated will be

Two conductors have the same resistance at $0\,^{\circ}C$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficient of their series combination is

All resistances in the figure are $1\,\Omega$ each. The value of current '$I$' is $\frac{a}{5}\,A$. The value of $a$ is

$A$ wire of resistance $R$ is bent into a circular ring of radius $r$. The equivalent resistance between two points $X$ and $Y$ on its circumference,where the central angle $XOY$ is $\alpha$ (in radians),is given by: