1. The problem statement, all variables and given/known data 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
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.
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.