For safety, the fuse wire used in the mains for household supply of electricity must be made of metal having

An electric bulb is marked $220 \mathrm{V}, 100 \mathrm{W}$. When it is connected across $110 \mathrm{V}$, its power is:

A uniform metallic wire of length $L$ is mounted in two configurations. In configuration $1$ (triangle), it is an equilateral triangle and a voltage, $V$ is applied to corners $A$ and $B$. In configuration $2$ (circle), it is bent in the form of a circle, and the potential $V$ is applied at diametrically opposite points $P$ and $Q$. The ratio of the power dissipated is configuration $1$ to configuration $2$ is.

A light bulb of resistance $R=16 \mathrm{\Omega }$ is attached in series with an infinite resistor network with identical resistances as shown below. A $10 \mathrm{V}$ battery derives a current in the circuit. What should be the value of $r$ such that the bulb dissipates about $1 \mathrm{W}$ of power?