$A$ total charge $Q$ flows across a resistor $R$ during a time interval $= T$ in such a way that the current vs. time graph for $0 \rightarrow T$ is like the loop of a sin curve in the range $0 \rightarrow \pi$ . The total heat generated in the resistor is

$(a)$ Consider circuit in figure. How much energy is absorbed by electrons from the initial state of no current (ignore thermal motion) to the state of drift velocity ?

$(b)$ Electrons give up energy at the rate of $R{I^2}\;$ per second to the thermal energy. What time scale would number associate with energy in problem $(a)$ ? $n = no$ of electron/volume $ = {10^{29}}{m^{ - 3}}$, length of circuit $= 10$ $cm$, cross-section $=$ $A = $ ${\left( {1\,mm} \right)^2}$

An electric kettle has two heating coils. When one of the coils is connected to an a.c. sotuce, the water in the kettle boils in $10$ minutes. When the other coil is used the w’ater boils in $40$ minutes. If both the coils are connected in parallel, the time taken by the same quantity of water to boil will be ...... $min$

A light bulb of resistance $R=16 \,\Omega$ is attached in series with an infinite resistor network with identical resistances $r$ as shown below. A $10 \,V$ battery drives current in the circuit. ............. $\Omega$ the value of $r$ such that the bulb dissipates about $1 \,W$ of power.

$n$ identical bulbs, each designed to draw a power $p$ from a certain voltage supply, are joined in series across that supply. The total power which they will draw is

How much energy in kilowatt hour is consumed in operating ten $50\, watt$ bulbs for $10$ hours per day in a month ($30$ days).