Electrical Voltage, a appliance problem

[helpphysics]

Homework Statement

Anyway can you please help me out with the following?

240V , 50 Hz electrical appliance is rated at 2 kW. It has a lagging power factor of 0.7
(a) What is appliances power factor when it is used on a 60Hz supply.
(b) What is supply voltage required to maintain appliance at its rated power when operated off a 60 Hz supply?


2. The attempt at a solution
No idea..!

Can you suggest some relevant equations and guidance?
Thanks in advance

 

[n.karthick]

First find Z of the load using the relation P=V^2/Z. Then using the given power factor you can find the reactance X=Zsin(theta). Let this be X1. Now find new X (X2) for 60 Hz. Remember X is directly proportional to frequency for a lagging circuit since it is inductive. From X2 you can calculate the parameters you want to know.

 

[helpphysics]

Hello, can you be bit more explanatory?
i am not getting anything !

 

[n.karthick]

You are asked to find pf on 60 Hz. You may remember that the impedance of the load Z=R+jX, where X is positive for inductive loads i.e., lagging pf and only X is dependent on frequency. Also pf=tan(X/R). Now if you change frequency of supply X changes proportionately. You know X=2*pi*f*L for inductive load. So for change in frequency from f1=50Hz to f2=60Hz , we have X2/X1=f2/f1. The first thing you have to do is find X1 i.e., X at 50 Hz using relations I mentioned earlier (Note pf=cos(theta) and so you can find theta). Then find X2 and from this since R is unchanged, you can find new pf.