How Do You Calculate Power Consumption in AC Circuits?

[math_04]

Homework Statement

In a domestic house, the voltage on the supply is 230V at angle 0 degrees. A number of household appliances are connected to the single phase supply causing a current of 20A at a power factor of 0.75 lagging to flow from the supply

a) What power is being consumed by the loads.

b) If energy is charged at 13 cents /KWh, how much would it cost to run the house for 24 hours?

c) If an electric radiator(resistive load) drawing 10A were connected in parallel with other loads, what total current would be drawn from the supply?

Homework Equations

Do I use Average Power = (Vrms)^2 /R. Thing is I don't know what Vrms is?

There is also P = Irms X Vrms cos (phi). I think cos phi = power factor = 0.75?

The Attempt at a Solution

So is the answer just P = 20 X 230 X 0.75? Also what if the angle was greater than 0 degrees? Does that matter i,e do I have to use a different equation.

Thanks, this is really hard, so many equations to remember. ill stick to DC circuit analysis any time of the day!

 

[buffordboy23]

Thing is I don't know what Vrms is?

No, but you can determine it. I assume your voltage of 230 volts represents the peak voltage of a sine wave for an alternating current. For a sine wave electric signal, Vrms = Vpeak/sqrt(2).

 

[mgb_phys]

230V is probably already the rms.
Usually you quote Vrms for an AC voltage and 230V is the standard Vrms for Europe.

 

[math_04]

Ohh so my above answer to P was right then? The one i mentioned in solution.

 

[Redbelly98]

Yes, if you mean "P = 20 X 230 X 0.75", you're correct.

I think cos phi = power factor = 0.75?

Also correct.

 

[ahmedibrahim7]

if the angle of the voltage not equal zero then
p=V(rms)*I(rms)*cos(phi)
power factor = cos(phi)=cos[theta(v)-theta(I)]
so if the voltage angle not equal zero it doesn't affect ur answer bec in power calculation u use the power factor which is constant so phi is also constant