Electrical Voltage, a appliance problem

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    Electrical Voltage
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Homework Help Overview

The discussion revolves around an electrical appliance rated at 240V and 2 kW with a lagging power factor of 0.7, specifically addressing its behavior when operated on a 60Hz supply instead of the original 50Hz. Participants are exploring how to determine the new power factor and the required supply voltage for the appliance under the changed frequency conditions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss finding the impedance of the load and its relationship to power factor and frequency. There are attempts to clarify how to calculate the new reactance at 60Hz and how it affects the power factor. Some participants express confusion about the equations and concepts involved.

Discussion Status

There is an ongoing exchange of ideas, with some participants providing equations and relationships to explore. However, there is also a request for further explanation and clarification, indicating that not all participants fully understand the proposed approaches.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the amount of direct assistance they can receive. The discussion highlights the need to understand the relationship between frequency and reactance for inductive loads.

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

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