In the above circuit, C = $${{\sqrt 3 } \over 2}$$$$\mu $$F, R₂ = 20 $$\Omega $$, L = $${{\sqrt 3 } \over {10}}$$ H and R₁ = 10 $$\Omega $$. Current in L-R₁ path is I₁ and in C-R₂ path it is I₂ . The voltage of A.C. source is given by, V = 200 $${\sqrt 2 }$$ sin (100 t) volts . The phase difference between I₁ and I₂ is :

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be :

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 $$\mu $$F. All values in the circuit are in $$\mu $$F.

A parallel plate capacitor with plates of area 1 m² each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is :

(Take $$\varepsilon $$₀ = 8.85 $$ \times $$ 10^$$-$$12 $${{{C^2}} \over {N - {m^2}}}$$)