Four equal resistances dissipate $5 \, W$ of power together when connected in series to a battery of negligible internal resistance. The total power dissipated in these resistances when connected in parallel across the same battery would be ........... $W$.

Two resistors with resistances $R_1$ and $R_2$ are connected in series and two capacitors with capacitances $C_1$ and $C_2$ are also connected in series. These two systems are connected to a battery of $EMF$ $\varepsilon$ as shown in the figure. The potential difference between points $a$ and $b$ is zero in the steady state if:

$A$ metallic conductor of irregular cross-section is as shown in the figure. $A$ constant potential difference is applied across the ends $(1)$ and $(2)$. Then:

The variation of current flowing through an electric heater with time,when it is switched on,is shown in the figure. Considering the change in resistance with temperature,which of the following graphs is correct?

Two cables of copper are of equal lengths. One of them has a single wire of area of cross-section $A$, while the other has $10$ wires of cross-sectional area $A / 10$ each. Determine their suitability for transporting $A.C.$ and $D.C.$

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 $10 \text{ A}$.
$(D)$ $Q = 2 \times 10^{-3} \text{ C}$.