Two coils of self inductance L₁ and L₂ are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :

The magnetic flux through a coil perpendicular to its plane is varying according to the relation $$\phi = (5{t^3} + 4{t^2} + 2t - 5)$$ Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will be,

If Electric field intensity of a uniform plane electromagnetic wave is given as $$E = - 301.6\sin (kz - \omega t){\widehat a_x} + 452.4\sin (kz - \omega t){\widehat a_y}{V \over m}$$. Then magnetic intensity 'H' of this wave in Am^$$-$$1 will be :

[Given : Speed of light in vacuum $$c = 3 \times {10^8}$$ ms^$$-$$1, Permeability of vacuum $${\mu _0} = 4\pi \times {10^{ - 7}}$$ NA^$$-$$2]

A sinusoidal voltage V(t) = 210 sin 3000 t volt is applied to a series LCR circuit in which L = 10 mH, C = 25 $$\mu$$F and R = 100 $$\Omega$$. The phase difference ($$\Phi $$) between the applied voltage and resultant current will be :