The temperature of the cold junction of a thermocouple is $0\,^oC$ and the temperature of the hot junction is $T\,^oC$. The thermo e.m.f. is given by the relation $E = AT - \frac{1}{2}BT^2$ (where $A = 16$ and $B = 0.08$). The temperature of inversion is ............... $^oC$.

$A$ torch bulb rated as $4.5\, W$,$1.5\, V$ is connected as shown in the figure. The $e.m.f.$ of the cell needed to make the bulb glow at full intensity is ................ $V$.

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

In Circuit-$1$ and Circuit-$2$ shown in the figures,$R_1=1 \Omega, R_2=2 \Omega$ and $R_3=3 \Omega$. $P_1$ and $P_2$ are the power dissipations in Circuit-$1$ and Circuit-$2$ when the switches $S_1$ and $S_2$ are in open conditions,respectively. $Q_1$ and $Q_2$ are the power dissipations in Circuit-$1$ and Circuit-$2$ when the switches $S_1$ and $S_2$ are in closed conditions,respectively. Which of the following statement$(s)$ is(are) correct?
$(A)$ When a voltage source of $6 V$ is connected across $A$ and $B$ in both circuits,$P_2 > P_1$.
$(B)$ When a constant current source of $2 A$ is connected across $A$ and $B$ in both circuits,$P_1 > P_2$.
$(C)$ When a voltage source of $6 V$ is connected across $A$ and $B$ in Circuit-$1$,$Q_1 > P_1$.
$(D)$ When a constant current source of $2 A$ is connected across $A$ and $B$ in both circuits,$Q_1 > Q_2$.

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 $= 10^3\, kg/m^3$)

In the given circuit, the internal resistance of the battery is $0.50\, \Omega$. What is the charge on the plates of the $5\, \mu F$ capacitor in $\mu C$?