An electric current passes through non-uniform cross-section wire made of homogeneous and isotropic material. If the $j_{\mathrm{A}}$ and $j_{\mathrm{B}}$ be the current densities and $E_{\mathrm{A}}$ and $E_{\mathrm{B}}$ be the electric field intensities at $A$ and $B$, respectively, then

 

A piece of copper and another of germanium are cooled from room temperature to $80 \mathrm{K}$. The resistance of 

All the edges of a block in cuboidal shape with parallel faces are equal. Its longest edge is twice its shortest edge. The ratio of the maximum to minimum resistance between parallel faces is

In which of the above cells, the potential difference between the terminals of a cell exceeds its emf?

In the figure a part of circuit is shown : 

Find the current flowing through the resistance $R_1$ of the circuit shown in figure if the resistances are equal to $R_1=10 \mathrm{\Omega }, R_2=20 \mathrm{\Omega }$, and $R_3=30 \mathrm{\Omega }$, and the potentials of points $1, 2$ and $3$ are equal to ${\mathrm{\phi }}_1 = 10 \mathrm{V}, {\mathrm{\phi }}_2 = 6 \mathrm{V},$ and ${\mathrm{\phi }}_3 = 5 \mathrm{V}$.