Power Factor Questions

In an a.c. circuit the e.m.f. ($e$) and the current ($i$) at any instant are given respectively by $e=E_0\sin \omega t$ and $i=I_0\sin (\omega t-\pi /2)$. The average power in the circuit over one cycle of a.c. is:

In an electrical circuit $R,L,C$ and an a.c voltage source are all connected in series. When $L$ is removed, the phase difference is $\pi /3$. If instead $C$ is removed, the phase difference is again $\pi /3$. The power factor of the circuit is:

The potential differences across the resistance, capacitance and inductance are $80\text{V},40\text{V}$ and $100\text{V}$ respectively in an L-C-R circuit. The power factor of this circuit is: