Two different metals are joined end to end. One end is kept at a constant temperature and the other end is heated to a very high temperature. The graph depicting the thermo $e.m.f.$ $(E)$ versus temperature $(t)$ is:

$A$ battery consists of a variable number $n$ of identical cells,each having electromotive force $E$ and internal resistance $r$,connected in series. The terminals of the battery are short-circuited,and the current $I$ is measured. Which one of the graphs below shows the relationship between $I$ and $n$?

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1 :$ The possibility of an electric bulb fusing is higher at the time of switching $ON.$
Statement $2:$ Resistance of an electric bulb when it is not lit up is much smaller than when it is lit up.

In an electrolysis experiment,a current $i$ passes through two different cells in series,one containing a solution of $CuSO_4$ and the other a solution of $AgNO_3$. The rate of increase of the weight of the cathodes in the two cells will be

The temperature at which thermo-emf is zero is

The thermoelectric electromotive force $e$ is given by $e = \alpha t - \frac{1}{2}\beta t^2$. If the temperature of the cold junction is $0 \, ^\circ C$,find the temperature of inversion $t_i$. (Given: $\alpha = 500.0 \, \mu V/^\circ C$,$\beta = 5.0 \, \mu V/^\circ C^2$)