For a cell of emf $2 \mathrm{V}$, a balance point is obtained for $50 \mathrm{cm}$ of the potentiometer wire. If the cell is shunted by a $2 \mathrm{\Omega }$ resistor, the balance is obtained across $40 \mathrm{cm}$ of the wire, then the internal resistance of the cell is

In the shown arrangement of a meter bridge, if $AC$ corresponding to null deflection of galvanometer is $x$, what would be its value if the radius of the wire $AB$ is doubled?

The following figure shows cross-sections through three long conductors of the same length and material, with a square cross-section of edge lengths as shown. Conductor $B$ will fit snugly within conductor $A$, and conductor $C$ will fit snugly within conductor $B$. Relationship between their end to end resistance is

An electric current passes through a non-uniform cross section of a wire made of homogeneous and isotropic material. If $j_{\mathrm{A}}$ 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,