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

A battery of $3.0\, V$ is connected to a resistor dissipating $0.5\, W$ of power. If the terminal voltage of the battery is $2.5\, V$ the power dissipated within the internal resistance is$.......W$

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.

Two bulbs consume same power when operated at $200\, V$ and $300\, V$ respectively. When these bulbs are connected in series across a $D.C$. source of $500\, V$, then

In the circuit shown in figure, the power which is dissipated as heat in the $6\,\Omega $ resistor is $6\,W$. What is the value of resistance $R$ in the circuit? ................ $\Omega$

In the circuit shown below, the resistances are given (in $\Omega$ ) and the battery is assumed ideal with emf equal to $3.0 \,V$. The resistor that dissipates the most power is