A heater is designed to operate with a power of $1000 \mathrm{~W}$ in a $100 \mathrm{~V}$ line. It is connected in combination with a resistance of $10 \Omega$ and a resistance $R$, to a $100 \mathrm{~V}$ mains as shown in figure. For the heater to operate at $62.5 \mathrm{~W}$, the value of $\mathrm{R}$ should be .................. $\Omega$.

A bulb of $100\, W$ is connected in parallel with an ideal inductance of $1\, H$. This arrangement is connected to a $90\,V$ battery through a switch. On pressing the switch, the

A $60\, watt$ bulb operates on $220\,V$ supply. The current flowing through the bulb is

For reduce in Ohmic loss transmission of electric power at very far distance of electric power is done at very high voltage ?

A student in a town in India, where the price per unit ( $1$ unit $=1 \,kWh$ ) of electricity is $₹ 5.00$, purchases a $1 \,kVA$ $UPS$ (uninterrupted power supply) battery. A day before the exam, $10$ friends arrive to the student's home with their laptops and all connect their laptops to the $UPS$. Assume that each laptop has a constant power requirement of $90 \,W$. Consider the following statements.

$I.$ All the $10$ laptops can be powered by the $UPS$, if connected directly.

$II.$ All the $10$ laptops can be powered, if connected using an extension box with a $3 \,A$ fuse.

$III.$ If all the $10$ friends use the laptop for $5 \,h$, then the cost of the consumed electricity is about $₹ 22.50.$

Select the correct option with the true statements.

In the circuit shown in figure, the $5\,\Omega $ resistance develops $20.00\,cal/s$ due to the current flowing through it. The heat developed in $2\,\Omega $ resistance (in $cal/s$ ) is