Assertion : When current through a bulb decreases by $0.5\%$, the glow of bulb decreases by $1\%$.

Reason : Glow (Power) which is directly proportional to square of current.

Two bulbs of $500\, watt$ and $200\, watt$ are manufactured to operate on $220\, volt$ line. The ratio of heat produced in $500\, W$ and $200\, W$, in two cases, when firstly they are joined in parallel and secondly in series, will be

In the circuit as shown in the figure, the heat produced by $6\, ohm$ resistance due to current flowing in it is $60$ calorie per second. The heat generated across $3\, ohm$ resistance per second will be ................. $calorie$

An electric bulb rated $50 \mathrm{~W}-200 \mathrm{~V}$ is connected across a $100 \mathrm{~V}$ supply. The power dissipation of the bulb is :

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.

In the circuit shown, the resistance $r$ is a variable resistance. If for $r = fR,$  the heat generation in $r$ is maximum then the value of $f$ is