In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be $$\sqrt {{x \over 2}} $$. The value of x is __________.

A cell, shunted by a 8 $$\Omega$$ resistance, is balanced across a potentiometer wire of length 3 m. The balancing length is 2 m when the cell is shunted by 4 $$\Omega$$ resistance. The value of internal resistance of the cell will be ____________ $$\Omega$$.

The current density in a cylindrical wire of radius 4 mm is 4 $$\times$$ 10⁶ Am^$$-$$2. The current through the outer portion of the wire between radial distances $${R \over 2}$$ and R is ____________ $$\pi$$ A.

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ____________ %.