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 ................... $^oC$.

$A$ room has an $AC$ running for $5$ hours a day at a voltage of $220$ $V$. The wiring of the room consists of $Cu$ wire of $1$ $mm$ radius and a length of $10$ $m$. Power consumption per day is $10$ commercial units. What fraction of it goes into Joule heating in the wires? What would happen if the wiring is made of aluminium of the same dimensions? $(\rho_{Cu} = 1.7 \times 10^{-8} \, \Omega m, \rho_{Al} = 2.7 \times 10^{-8} \, \Omega m)$

Two heaters $A$ and $B$ have power ratings of $1 \text{ kW}$ and $2 \text{ kW}$,respectively. These two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is:

Two electric bulbs marked $40\,W, 220\,V$ and $60\,W, 220\,V$ are connected in series across a $220\,V$ supply,resulting in an effective power $P_1$. When they are connected in parallel across the same $220\,V$ supply,the effective power is $P_2$. The ratio $\frac{P_1}{P_2}$ is:

In a copper voltameter,the mass of copper deposited in $6 \, \text{min}$ is $m \, \text{g}$. If the current-time graph is as shown in the figure,the electrochemical equivalent of copper will be:

If in the circuit shown below,the internal resistance of the battery is $1.5 \, \Omega$ and $V_P$ and $V_Q$ are the potentials at $P$ and $Q$ respectively,what is the potential difference between the points $P$ and $Q$?