In Circuit-$1$ and Circuit-$2$ shown in the figures, $R_1=1\mathrm{\Omega },R_2=2\mathrm{\Omega }$ and $R_3=3\mathrm{\Omega }$.
$P_1$ and $P_2$ are the power dissipations in Circuit-$1$ and Circuit-$2$ when the switches $S_1$ and $S_2$ are in open conditions, respectively.
$Q_1$ and $Q_2$ are the power dissipations in Circuit-$1$ and Circuit-$2$ when the switches $S_1$ and $S_2$ are in closed conditions, respectively.

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Which of the following statement(s) is(are) correct?

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?

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.

Consider the following two circuits

$\left[A\right] :$ $20$ bulbs are connected in series to a power supply line

$\left[B\right] :$ $20$ bulbs identical to $\left[A\right]$ are connected in a parallel circuit to an identical power supply line

Identify which of the following is not true

A zener diode having zener voltage $8 V$ and power dissipation rating of $0.5 W$ is connected across a potential divider arranged with maximum potential drop across zener diode is as shown in the diagram. The value of protective resistance $R_p$ is _____$\mathrm{\Omega }.$