Find out the expression for heat produced in a conductor due to flow of current.

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?

In the circuit shown, the heat produced in $5 \mathrm{\Omega }$ resistor is $10 \mathrm{cal} {\mathrm{s}}^{-1}$. The heat produced per sec in $4 \mathrm{\Omega }$ resistor will be

$ADC$ source with internal resistance $R_0$ is connected to circuit as shown in the figure. The value of $R$ for which the power generated in the circuit is the maximum 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 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.