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

An ammeter reads upto $$1$$ ampere. Its internal resistance is $$0.81$$ $$ohm$$. To increase the range to $$10$$ $$A$$ the value of the required shunt is

The nagative $$Zn$$ pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by $$0.13g$$ in $$30$$ minutes. If the electrochemical equivalent of $$Zn$$ and $$Cu$$ are $$32.5$$ and $$31.5$$ respectively, the increase in the mass of the positive $$Cu$$ pole in this time is

A $$3$$ volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current $${\rm I}$$, in the circuit will be