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.
A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ___________ nJ.
The height of a transmitting antenna at the top of a tower is 25 m and that of receiving antenna is, 49 m. The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is K$$\sqrt5$$ $$\times$$ 102 m. The value of K is ___________.
(Assume radius of Earth is 64 $$\times$$ 10+5 m) [Calculate upto nearest integer value]