Three resistances of magnitude $2\,\Omega$,$3\,\Omega$,and $5\,\Omega$ are connected in parallel to a battery of $10\,V$ and of negligible resistance. The potential difference across the $3\,\Omega$ resistance will be ............... $V$.

An electric kettle has two filaments. The first filament boils a certain amount of water in $10 \text{ minutes}$ and the second filament boils it in $15 \text{ minutes}$. If both filaments are connected in parallel,the water will boil in .............. minutes.

$A$ wire of resistance $R$ is bent to form a circular ring. Find the equivalent resistance between two points $X$ and $Y$ on its circumference. (The angle $XOY = \alpha$ is given.)

$A$ wire of resistance $12 \,\Omega$ is bent into a circle. What is the equivalent resistance between two diametrically opposite points in $\Omega$?

Four resistors,$100 \Omega, 200 \Omega, 300 \Omega$ and $400 \Omega$ are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square (in $Omega$)?

An electric heater and an electric bulb are rated $500\, W, 220\, V$ and $100\, W, 220\, V$ respectively. Both are connected in series to a $220\, V$ $a.c.$ mains. The current in the circuit when both are connected in series is ................ $A$.