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 ............. $min$.

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.

Let there be $n$ resistors $R_1, \dots, R_n$ with $R_{\max} = \max \{R_1, \dots, R_n\}$ and $R_{\min} = \min \{R_1, \dots, R_n\}$. Show that when they are connected in parallel,the resultant resistance $R_p < R_{\min}$ and when they are connected in series,the resultant resistance $R_s > R_{\max}$. Interpret the result physically.

Two bulbs,one of $200 \ V, 60 \ W$ and the other of $200 \ V, 100 \ W$,are connected in series to a $200 \ V$ supply. The power consumed will be ................ $W$.

Two bulbs,one of $50\, W$ and another of $25\, W$,are connected in series to the mains. The ratio of the currents through them is:

Referring to the figure below,the effective resistance of the network is