The three resistances $A, B$ and $C$ have values $3R, 6R$ and $R$ respectively. When some potential difference is applied across the network,the thermal powers dissipated by $A, B$ and $C$ are in the ratio

$A$ cell of negligible internal resistance and $e.m.f.$ $2 \ V$ is connected to a series combination of $2 \ \Omega$,$3 \ \Omega$,and $5 \ \Omega$ resistors. The potential difference in volts between the terminals of the $3 \ \Omega$ resistor is:

Find the current in the $3\,\Omega$ resistance in the given circuit.

$A$ $16 \ \Omega$ wire is bent to form a square loop. $A$ $9 \ V$ battery with internal resistance $1 \ \Omega$ is connected across one of its sides. If a $4 \ \mu F$ capacitor is connected across one of its diagonals,the energy stored by the capacitor will be $\frac{x}{2} \ \mu J$,where $x = . . . . . . .$

Two light bulbs in the circuit have ratings $A\,[24\ V, 48\ W]$ and $B\,[24\ V, 36\ W]$ as shown in the figure.

The thermo $e.m.f.$ of a thermocouple is $25\,\mu V/^{\circ}C$ at room temperature. $A$ galvanometer of $40\,\Omega$ resistance, capable of detecting current as low as $10^{-5}\,A$, is connected with the thermocouple. The smallest temperature difference that can be detected by this system is ................ $^{\circ}C$.