The thermo e.m.f $E$ in volts of a certain thermocouple is found to vary with temperature difference $\mathrm{\theta }$ in $°\mathrm{C}$ between the two junctions according to the relation. $\mathit{\text{E}}=\text{30}\mathrm{\theta }-\frac{{\theta }^2}{\text{15}}$. The neutral temperature for the thermocouple will be,

The figure shows a part of a closed circuit. If the current flowing through it is $2 \mathrm{A}$ then $V_B-V_A$ is _______

In the network shown, the equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is $\frac{4}{3}\mathrm{\Omega }$, find the value of $\mathrm{r}$.

Shown in the figure is a semicircular metallic strip that has thickness $t$ and resistivity $\rho$. Its inner radius is $R_1$ and outer radius is $R_2$. If a voltage $V_0$ is applied between its two ends, a current $I$ flows in it. In addition, it is observed that a transverse voltage $\mathrm{\Delta }V$ develops between its inner and outer surfaces due to purely kinetic effects of moving electrons (ignore any role of the magnetic field due to the current). Then (figure is schematic and not drawn to scale)

Two cells of the same EMF $E$ but different internal resistances $r_1$ and $r_2$ are connected in series with an external resistance $R$ as shown in the figure. The terminal potential difference across, the second cell is found to be zero. The external resistance $R$ must then be:

The potential difference between points $A$ and $B$ of adjoining figure is