In series LCR circuit, at resonance the peak value of current will be [$$\mathrm{E_0}$$ is peak emf, R is resistance, $$\omega \mathrm{L}$$ is inductive reactance and $$\omega \mathrm{C}$$ is capacitive]

An alternating e.m.f. is $$\mathrm{e}=\mathrm{e}_0 \sin \omega \mathrm{t}$$. In what time the e.m.f. will have half its maximum value, if '$$\mathrm{e}$$' starts from zero? ($$\mathrm{T}=$$ time period, $$\sin 30^{\circ}=0.5$$)

A step up transformer operates on $$220 \mathrm{~V}$$ and supplies current of $$2 \mathrm{~A}$$. The ratio of primary and secondary windings is $$1: 20$$. The current in the primary is

In the part of an a.c. circuit as shown, the resistance $$R=0.2 \Omega$$. At a certain instant $$(\mathrm{V_A-V_B})= 0.5 \mathrm{~V}, \mathrm{I}=0.5 \mathrm{~A}$$ and $$\frac{\Delta \mathrm{I}}{\Delta \mathrm{t}}=8 \mathrm{~A} / \mathrm{s}$$. The inductance of the coil is