Water boils in an electric kettle in $20$ minutes after being switched on. Using the same main supply,the length of the heating element should be . . . . . . to . . . . . . times of its initial length if the water is to be boiled in $15$ minutes.

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true?
$(A)$ The temperature distribution over the filament is uniform
$(B)$ The resistance over small sections of the filament decreases with time
$(C)$ The filament emits more light at higher band of frequencies before it breaks up
$(D)$ The filament consumes less electrical power towards the end of the life of the bulb

An electric lamp is marked $60\, W$, $230\, V$. The cost of $1\, kWh$ of energy is Rs. $1.25$. The cost of using this lamp for $8$ hours a day for $30$ days is Rs. ...............

$A$ $500\, W$ heating unit is designed to operate from a $115\, V$ line. If the line voltage drops to $110\, V$,the percentage drop in heat output will be ............... $\%$

In an electric heater, $4\, A$ current passes for $1\, \text{minute}$ at a potential difference of $250\, V$. The power of the heater and the energy consumed will be, respectively:

If a power of $100\, W$ is being supplied across a potential difference of $200\, V$,the current flowing is ............ $A$.