$A$ thermocouple uses Bismuth and Tellurium as the dissimilar metals. The sensitivity of Bismuth is $-72\,\mu V/{^oC}$ and that of Tellurium is $500\,\mu V/{^oC}$. If the difference between hot and cold junction is $100\,{^oC}$, then the maximum output will be ............... $mV$.

In the circuit shown below,the resistance and the emf source are both variable. The graph of seven readings of the voltmeter and the ammeter ($V$ and $I$,respectively) for different settings of resistance and the emf,taken at equal intervals of time $\Delta t$,are shown below by the dots connected by the curve $EFGH$. Consider the internal resistance of the battery to be negligible and the voltmeter and ammeter to be ideal devices. (Take $R_0 = \frac{V_0}{I_0}$). Then,the plot of the resistance as a function of time corresponding to the curve $EFGH$ is given by:

$A$ wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to current,the temperature of the wire is raised by $\Delta T$ in a time $t$. $A$ number $N$ of similar cells is now connected in series with a wire of the same material and cross-section but of length $2L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time $t$. The value of $N$ is

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

Two wires '$A$' and '$B$' of the same material have their lengths in the ratio $1 : 2$ and radii in the ratio $2 : 1$. The two wires are connected in parallel across a battery. The ratio of the heat produced in '$A$' to the heat produced in '$B$' for the same time is