In an a.c. circuit, the instantaneous e.m.f. and current are given by
e = 100 sin 30 t
i = 20 sin $$\left( {30t - {\pi \over 4}} \right)$$
In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively

For an RLC circuit driven with voltage of amplitude vm and frequency $${\omega _0}$$ = $${1 \over {\sqrt {LC} }}$$ the current exhibits resonance. The quality factor, Q is given by :

An EM wave from air enters a medium. The electric fields are
$$\overrightarrow {{E_1}} $$ = $${E_{01}}\widehat x\cos \left[ {2\pi v\left( {{z \over c} - t} \right)} \right]$$ in air and $$\overrightarrow {{E_2}} $$ = $${E_{02}}\widehat x\cos \left[ {k\left( {2z - ct} \right)} \right]$$ in medium, where the wave number k and frequency $$\nu $$ refer to their values in air. The medium is non-magnetic. If $${\varepsilon _{{r_1}}}$$ and $${\varepsilon _{{r_2}}}$$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

A copper rod of mass m slides under gravity on two smooth parallel rails, with separation l and set at an angle of $$\theta $$ with the horizontal. At the bottom rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the igure. The terminal speed of the copper rod is :