Power factor and frequency change

[DT71]

Homework Statement

240V,50 Hz electrical appliance is rated at 2KW and has a lagging power factor of0.7.
a)Determine the appliance's power factor when it is used on a 60Hz supply?
b)Calculate the supply voltage required to maintain the appliance at its rated power when operated off a 60Hz supply?

Homework Equations

p.f.=P/S
S^2=P^2+Q^2 to obtain Q
S=VsI to obtain I
Z=Vs/I to obtain Z
p.f. = R/Z to obtain R
Z^2=R^2+Xl^2 to obtain Xl
Xl=2pifL to obtain L at 50Hz

The Attempt at a Solution

I have done the above then used the value for L in Xl=2pifL at 60 Hz but not sure were to go from here.

 

[n.karthick]

As you have already found Xl at 60 Hz you can find power factor at 60 Hz from value of new Z and R (Note R is unchanged)

Since you know Z and P (rated power) you can find V

 

[DT71]

Thanks, I get the first section now but I don't see how I can work out the supply voltage using the new Z and the rated power.

 

[DT71]

should i be using P=V^2/Z

 

[n.karthick]

Note V^2/Z gives the apparent power S.

 

[DT71]

I'm confused now, how do I calculate the supply voltage required to maintain the appliance at its rated power at 60Hz.

I have the rated power and the impedence at 60Hz.

 

[n.karthick]

Hi, you know P and Z, from Z you can find p.f.
From above values you can find S. Once you know S you can find V.

 

[DT71]

I have worked out the pf to be 0.63
P(rated power) = 2000 w
Z=22.31 ohms

Would it be correct to use P(rated power)= V^2/R as R remains the same to obtain V(supply voltage)