A $100\, W$ bulb $B_1$, and two $60\,W$ bulbs $B_2$ and $B_3$, are connected to a $250\, V$ source, as shown in the figure. Now $ W_1, W_2$ and $W_3$ are the output powers of the bulbs $B_1, B_2$ and $B_3$, respectively. Then

The power dissipated in the circuit shown in the figure is $30\, Watts$. The value of $R$ is ............. $\Omega$

Two electric bulbs ($60\,W$ and $100\,W$ respectively) are connected in series. The current passing through them is

An electric bulb rated as $200\, {W}$ at $100 \,{V}$ is used in a circuit having $200\, {V}$ supply. The resistance $'R'$ that must be put in series with the bulb so that the bulb delivers the same power is $.....\,\Omega$

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.

A bulb has specification of one kilowatt and $250\, volts$, the resistance of bulb is .................. $\Omega$