The electrochemical equivalent of a metal is $${3.35109^{ - 7}}$$ $$kg$$ per Coulomb. The mass of the metal liberated at the cathode when a $$3A$$ current is passed for $$2$$ seconds will be

The thermo $$emf$$ of a thermocouple varies with temperature $$\theta $$ of the hot junction as $$E = a\theta + b{\theta ^2}$$ in volts where the ratio $$a/b$$ is $${700^ \circ }C.$$ If the cold junction is kept at $${0^ \circ }C,$$ then the neutral temperature is

A material $$'B'$$ has twice the specific resistance of $$'A'.$$ A circular wire made of $$'B'$$ has twice the diameter of a wire made of $$'A'$$. Then for the two wires to have the same resistance, the ratio $${l \over B}/{l \over A}$$ of their respective lengths must be

The Kirchhoff's first law $$\left( {\sum i = 0} \right)$$ and second law $$\left( {\sum iR = \sum E} \right),$$ where the symbols have their usual meanings, are respectively based on