Suppose the drift velocity $v_d$ in a material varies with the applied electric field $E$ as $v_d \propto \sqrt{E}$. Then the $V-I$ graph for a wire made of such a material is best given by:

The cold junction of a thermocouple is at $10\,^{\circ}\text{C}$. When the temperature of the hot junction is $530\,^{\circ}\text{C}$,no thermo-emf is produced. What is the neutral temperature in $^{\circ}\text{C}$?

As the temperature of the hot junction of a thermocouple is increased (while the cold junction is at a constant temperature), the thermo $e.m.f.$

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

Due to cold weather,a $1\, m$ water pipe of cross-sectional area $1\, cm^2$ is filled with ice at $-10^{\circ}C$. Resistive heating is used to melt the ice. $A$ current of $0.5\, A$ is passed through a $4\, k\Omega$ resistance. Assuming that all the heat produced is used for melting,what is the minimum time required? (In $s$)
(Given: latent heat of fusion for water/ice $= 3.33 \times 10^5\, J/kg$,specific heat of ice $= 2 \times 10^3\, J/(kg\cdot K)$ and density of ice $= 10^3\, kg/m^3$)

There are two electric bulbs of $40\, W$ and $100\, W$. Which one will be brighter when first connected in series and then in parallel?