The equivalent resistance of the following infinite network of resistances is

Two bulbs rated $25 \ W - 220 \ V$ and $100 \ W - 220 \ V$ are connected in series to a $440 \ V$ supply. Which of the following happens?

$A$ uniform metallic wire carries a current of $2\,A$ when a $3.4\,V$ battery is connected across it. The mass of the uniform metallic wire is $8.92 \times 10^{-3}\,kg$,its density is $8.92 \times 10^3\,kg/m^3$,and its resistivity is $1.7 \times 10^{-8}\,\Omega\cdot m$. The length of the wire is $l = \dots\dots\dots\dots\,m$.

Two electric bulbs with ratings $25\, W - 220\, V$ and $100\, W - 220\, V$ are connected in series to a $440\, V$ supply. Which bulb will fuse?

What is the maximum number of $50 \, W - 100 \, V$ bulbs that can be connected in parallel to a battery of $120 \, V$ and $10 \, \Omega$ internal resistance so that they glow with maximum intensity?

$A$ $16 \ \Omega$ wire is bent to form a square loop. $A$ $9 \ V$ battery with internal resistance $1 \ \Omega$ is connected across one of its sides. If a $4 \ \mu F$ capacitor is connected across one of its diagonals,the energy stored by the capacitor will be $\frac{x}{2} \ \mu J$,where $x = . . . . . . .$