In an a.c. circuit the e.m.f. ($$\varepsilon $$) and the current

(i)  at any instant are given respectively by
$$\varepsilon $$ = E₀sin$$\omega $$t,   $$i$$ = $$I$$₀sin($$\omega $$t $$-$$ $$\phi $$)

The average power in the circuit over one cycle of a.c. is

The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux $$\phi $$ linked with the primary coil is given by $$\phi $$ = $$\phi $$₀ + 4t, where $$\phi $$ is webers, t is time in seconds and $$\phi $$₀ is a constant, the output voltage across the secondary coil is

What is the value of inductance L for which the current is maximum in a series LCR circuit with C = 10 $$\mu $$F and $$\omega $$ = 1000 s^$$-$$1 ?

A transformer is used to light a 100 W and 110 V lamp from a 220 V mains. If the main current is 0.5 amp, the efficiency of the transformer is approximately