The expression for thermo $e.m.f.$ in a thermocouple is given by the relation $E = 40\theta - \frac{\theta^2}{20}$,where $\theta$ is the temperature difference of two junctions. For this,the neutral temperature will be ................... $^oC$.

The maximum power delivered to resistance $R$ is ............... $W$.

$A$ student measures the terminal potential difference $(V)$ of a cell (of $emf \; \varepsilon$ and internal resistance $r$) as a function of the current $(I)$ flowing through it. The slope and intercept of the graph between $V$ and $I$,respectively,are equal to:

First,a set of $n$ equal resistors of $10 \; \Omega$ each are connected in series to a battery of emf $20 \; V$ and internal resistance $10 \; \Omega$. $A$ current $I$ is observed to flow. Then,the $n$ resistors are connected in parallel to the same battery. It is observed that the current is increased $20$ times. The value of $n$ is .... .

$A$ wire of resistance $10\, \Omega$ is bent into a circle. $P$ and $Q$ are two points on the circumference of the circle that divide the circle into a quadrant. When these two points are connected to a battery of $3\, V$ and internal resistance $1\, \Omega$, the currents passing through the two parts of the circle are:

$A$ $3\,^oC$ rise in temperature is observed in a conductor by passing a certain current. When the current is doubled,the rise in temperature will be ............. $^oC$.