An e.m.f. $$E=4 \cos (1000 t)$$ volt is applied to an LR circuit of inductance $$3 \mathrm{~mH}$$ and resistance $$4 ~\Omega$$. The maximum current in the circuit is

An alternating voltage of frequency '$$\omega$$' is induced in electric circuit consisting of an inductance '$$L$$' and capacitance '$$C$$', connected in parallel. Then across the inductance coil

The reactance of capacitor at $$50 \mathrm{~Hz}$$ is $$5 \Omega$$. If the frequency is increased to $$100 \mathrm{~Hz}$$, the new reactance is

The coil of an a.c. generator has 100 turns, each of cross-sectional area $$2 \mathrm{~m}^2$$. It is rotating at constant angular speed $$30 ~\mathrm{rad} / \mathrm{s}$$, in a uniform magnetic field of $$2 \times 10^{-2} \mathrm{~T}$$. If the total resistance of the circuit is $$600 ~\Omega$$ then maximum power dissipated in the circuit is