An electric kettle has two coils. When one of these is switched on,the water in the kettle boils in $6\,min$. When the other coil is switched on,the water boils in $3\,min$. If the two coils are connected in series,the time taken to boil the water in the kettle is ............. $min$.

In the given circuit,the equivalent resistance between the points $A$ and $B$ is (in $ohm$):

$A$ circular coil of total resistance $40 \Omega$ has two points '$P$' and '$Q$' on its circumference. The arc length between '$P$' and '$Q$' is such that the coil is divided into two parts with resistances $30 \Omega$ and $10 \Omega$. These points are connected to a $16 \text{ V}$ battery with an internal resistance of $0.5 \Omega$. What is the value of the current '$I$' flowing through the circuit (in $\text{ A}$)?

Eight resistances each of resistance $5\,\Omega$ are connected in the circuit as shown in the figure. The equivalent resistance between $A$ and $B$ is

The equivalent resistance between the points $A$ and $D$ is ................ $\Omega$.

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: