$A$ 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 in configuration $1$ to configuration $2$ is

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

Two $220\; V, 100\; W$ bulbs are connected first in series and then in parallel. Each time the combination is connected to a $220\; V\; AC$ supply line. The power drawn by the combination in each case respectively will be

Two different metals are joined end to end. One end is kept at a constant temperature and the other end is heated to a very high temperature. The graph depicting the thermo $e.m.f.$ $(E)$ versus temperature $(t)$ is:

If $E = at + bt^2$,what is the temperature of inversion?

The thermo emf of a hypothetical thermocouple varies with the temperature $\theta$ of the hot junction as $E = a\theta + b\theta^2$ in volts,where the ratio $a/b$ is $700^{\circ}C$. If the cold junction is kept at $0^{\circ}C$,then the neutral temperature is: