In the following circuit, the battery has an emf of  $2\mathrm{V}$ and an internal resistance of $\frac{2}{3}\  \Omega$. The power consumption in the entire circuit is$..... W.$

Heater of electric kettle is made of a wire of length $L$ and diameter $d$. It takes $4$ minutes to raise the temperature of $0.5 \ kg$ water by $40\ K$. This heater is replaced by a new heater having two wires of the same material, each of length $L$ and diameter $2 d$. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by $40K$ ?

$(A)$ $4$ if wires are in parallel

$(B)$ $2$ if wires are in series

$(C)$ $1$ if wires are in series

$(D)$ $0.5$ if wires are in parallel.

The maximum power delivered to resistance $R$ is  ............... $W$

A resistor develops $300 \,J$ of thermal energy in $15 \,s$, when a current of $2\, A$ is passed through it. If the current increases to $3 \,A$, the energy developed in $10\,\,s$  is........$J.$

A time varying current $i$ is passed through a resistance $R$ as shown in figure. The total heat generated in the resistance is

$A$ 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