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:

The Thomson coefficient of a conductor is $10 \mu V/K$. The two ends of the conductor are kept at $50^{\circ} C$ and $60^{\circ} C$, respectively. The amount of heat absorbed by the conductor when a charge of $10 C$ flows through it is:

Three wires of copper,iron,and nickel are joined to form three junctions as shown in the figure. When the temperature of junction $1$ is kept at $50\,^{\circ}\text{C}$ with the other two junctions at $0\,^{\circ}\text{C}$,the sensitive galvanometer gives a deflection of $14$ divisions. When the temperature of junction $3$ is kept at $50\,^{\circ}\text{C}$,with the other two junctions at $0\,^{\circ}\text{C}$,the galvanometer gives a deflection of $11$ divisions. Then the deflection given by the galvanometer,when the temperature of junction $2$ is kept at $50\,^{\circ}\text{C}$,with the other two junctions at $0\,^{\circ}\text{C}$,will be (in $div$)

Amount of electricity required to pass through the ${H_2O}$ voltmeter so as to liberate $11.2 \, L$ of hydrogen will be ............ $F$.

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 ............... $^oC$.

If for a thermocouple ${T_n}$ is the neutral temperature,${T_c}$ is the temperature of the cold junction,and ${T_i}$ is the temperature of inversion,then: