In the circuit of the adjoining figure,the current through the $12 \ \Omega$ resistor will be ................ $A$.

$A$ wire of resistance $10 \, \Omega$ is bent to form a circle. $P$ and $Q$ are points on the circumference of the circle dividing it into a quadrant and are connected to a battery of $3 \, V$ and internal resistance $1 \, \Omega$ as shown in the figure. The currents in the two parts of the circle are

The temperature dependence of resistances of $Cu$ and undoped $Si$ in the temperature range $300-400 \ K$,is best described by

One junction of a certain thermoelectric couple is at a fixed temperature $T_r$ and the other junction is at temperature $T$. The thermo-electromotive force for this is expressed by $E=k(T-T_r)[T_0-\frac{1}{2}(T+T_r)]$. At temperature $T=\frac{1}{2} T_0$, the thermoelectric power is

The Thomson coefficient of a conductor is $10\,\mu V/K$. The two ends of the conductor are maintained 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:

Two wires with resistances $R$ and $2R$ are connected in parallel. The ratio of heat generated in $2R$ and $R$ is: