Why do we want higher power factor in ac motors?
But, I am going to pay for only real power? Isn't it right? So why do I want power factor to be high?


If you are a small user you will only pay for real power. Your poor power factor will make little difference to the electrical grid. It is not worthwhile for the power company to meter you for the reactive power (kVArh).

If you are a large user and your power factor is poor you will cause problems for the grid:


Your reactive load will cause higher currents to flow than would flow for the same (real) power in a resistive load. This will cause increased voltage drop along the supply line. If you are only metered for real power (kWh) then the power company has to bear the loss.
To solve this a dual meter is installed for large users. This measures both kWh and kVArh. Typically there is no surcharge if the power factor is kept >= 0.95 but penalties are applied if too much reactive power is used.



  To make power factor high, I have to increase the series resistance on the inductor ...


No, we can correct for inductive power factor by adding capacitance across the supply.



Figure 1. Adding power-factor correction capacitors can partially (as in this example), fully or over-correct inductive power-factor. Source: PowerFactor.us.

In industrial applications a bank of power-factor capacitors is typically installed at the main distribution panel. A controller monitors the incoming voltage and current, calculates the power-factor and switches in contactors to connect the capacitors across the supply. Since most industrial premises are three-phase the capacitors are supplied in delta configuration inside a three-terminal metal case.



Figure 2. An industrial power-factor correction bank with controller (mounted on door), fuses, contactors (relays) and capacitors. Source: Direct Industry.