In the following circuit composed of identical resistors,across which terminals would you connect a battery in order to dissipate energy in all resistors?

The currents $i_1$ and $i_2$ through the resistors $R_1 (= 10\,\Omega)$ and $R_2 (= 30\,\Omega)$ in the circuit diagram with $E_1 = 3\,V, E_2 = 3\,V$ and $E_3 = 2\,V$ are respectively:

$A$ thermocouple of resistance $1.6\,\Omega$ is connected in series with a galvanometer of $8\,\Omega$ resistance. The thermocouple develops an e.m.f. of $10\,\mu V$ per degree temperature difference between two junctions. When one junction is kept at $0\,^{\circ}C$ and the other in a molten metal,the galvanometer reads $8\,mV$. The temperature of the molten metal,when e.m.f. varies linearly with temperature difference,will be ............ $^{\circ}C$.

If the resistance of each edge of a cube-shaped wire frame as shown in the figure below is $R$,then the resistance between points $1$ and $7$ is

$A$ battery of $e.m.f.$ $10 \, V$ and internal resistance $3 \, \Omega$ is connected to a resistor $R$ as shown in the figure. If the current in the circuit is $0.5 \, A$,then the resistance of the resistor $R$ will be ............. $\Omega$.

In the given circuit,the potential difference between points $P$ and $Q$ is . . . . . . (in $\text{ V}$)