Power factor and frequency change

1. Nov 25, 2010

DT71

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

2. Relevant 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

3. 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.

2. Nov 26, 2010

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

3. Nov 26, 2010

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.

4. Nov 26, 2010

DT71

should i be using P=V^2/Z

5. Nov 26, 2010

n.karthick

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

6. Nov 26, 2010

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.

7. Nov 26, 2010

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.

8. Nov 26, 2010

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)