Two coils require $20$ minutes and $60$ minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be________ $min$

In the figure shown the power generated in $y$ is maximum when $y = 5\,\Omega $. Then $R$ is

A coil develops heat of $800\, cal/sec$. When $20\, volts$ is applied across its ends. The resistance of the coil is .............. $\Omega$ ($1$ $cal$ = $4.2$ $joule$)

Two bulbs $X$ and $Y$ having same voltage rating and of power $40\, watt$ and $60\, watt$ respectively are connected in series across a potential difference of $300\, volt$, then

Heater of electric kettle is made of a wire of length $L$ and diameter $d$. It takes $4$ minutes to raise the temperature of $0.5 \ kg$ water by $40\ K$. This heater is replaced by a new heater having two wires of the same material, each of length $L$ and diameter $2 d$. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by $40K$ ?

$(A)$ $4$ if wires are in parallel

$(B)$ $2$ if wires are in series

$(C)$ $1$ if wires are in series

$(D)$ $0.5$ if wires are in parallel.

A battery of internal resistance $4\, ohm$ is connected to the network of resistance as hown.  In the order that the maximum power can be delivered to the network, the value of $R$ in ohm should be :-