A fully charged capacitor has a capacitance $$'C'$$. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity $$'s'$$ and mass $$'m'.$$ If the temperature of the block is raised by $$'\Delta T',$$ the potential difference $$'v'$$ across the capacitance is

Two thin, long, parallel wires, separated by a distance $$'d'$$ carry a current of $$'i'$$ $$A$$ in the same direction. They will

A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

In the circuit, the galvanometer $$G$$ shows zero deflection. If the batteries $$A$$ and $$B$$ have negligible internal resistance, the value of the resistor $$R$$ will be -