The battery shown in the figure has an $e.m.f.$ $E$ and internal resistance $r$. The current in the circuit can be varied by sliding the contact $J$. If at any instant the current flowing through the circuit is $I$,the potential difference between the terminals of the cell is $V$,and the thermal power generated in the cell is equal to $\eta$ fraction of the total electrical power generated in it,then which of the following graphs is correct?

At time $t = 0$,terminal $A$ in the circuit shown in the figure is connected to $B$ by a key and alternating current $I(t) = I_0 \cos(\omega t)$,with $I_0 = 1 \text{ A}$ and $\omega = 500 \text{ rad s}^{-1}$ starts flowing in it with the initial direction shown in the figure.
At $t = \frac{7\pi}{6\omega}$,the key is switched from $B$ to $D$. Now onwards only $A$ and $D$ are connected. $A$ total charge $Q$ flows from the battery to charge the capacitor fully. If $C = 20 \mu\text{F}$,$R = 10 \Omega$ and the battery is ideal with emf of $50 \text{ V}$,identify the correct statement$(s)$.
$(A)$ Magnitude of the maximum charge on the capacitor before $t = \frac{7\pi}{6\omega}$ is $1 \times 10^{-3} \text{ C}$.
$(B)$ The current in the left part of the circuit just before $t = \frac{7\pi}{6\omega}$ is clockwise.
$(C)$ Immediately after $A$ is connected to $D$,the current in $R$ is $10 \text{ A}$.
$(D)$ $Q = 2 \times 10^{-3} \text{ C}$.

If the temperature of the cold junction decreases,then the neutral temperature

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

$A$ cell of emf $E$ is connected to a resistance $R_{1}$ for time $t$ and the amount of heat generated in it is $H$. If the resistance $R_{1}$ is replaced by another resistance $R_{2}$ and is connected to the cell for the same time $t$, the amount of heat generated in $R_{2}$ is $4H$. Then the internal resistance $r$ of the cell is:

$A$ student measures the terminal potential difference $(V)$ of a cell (of $emf \; \varepsilon$ and internal resistance $r$) as a function of the current $(I)$ flowing through it. The slope and intercept of the graph between $V$ and $I$,respectively,are equal to: