A single-phase motor with a rated output power of 40 kW at an efficiency of 80% and 0.6 lagging power factor is connected to an electrical power supply rated at 220 volt, 50Hz. The single-phase motor can be represented by a series resistor-inductor circuit as shown in Fig. 1a.


(i) Find the input current to the motor. [5 marks]


(ii) Find the values of the resistor ‘R’ and the inductor ‘L’ respectively.

I cannot find the related formula in my notes, what am I supposed to do to solve this question?

 

Formulas are not available for all engineering problems. So what you are "supposed to do" is determine the equations yourself. That's what engineers are for. If there were formulas available for all problems, then you likely wouldn't need engineers -- a computer could do the work.
So do you understand the relation between power factor, circuit power, motor efficiency, and circuit current?
If you know that, you can solve the problem.
If not, you need to study that.