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Reactive Power Calculations — Parallax Forums

Reactive Power Calculations

william chanwilliam chan Posts: 1,326
edited 2008-08-23 21:09 in General Discussion
Hi,

Let's say I have a 1uf 400V capacitor in series with a 10ohm resistor.
If I connect this pair directly to AC 240v 50Hz supply, how many watts would it consume?

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Comments

  • skylightskylight Posts: 1,915
    edited 2008-08-23 15:34
    The capacitive reactance (Xc) in ohms is found by:

    1 / (2 * pi * f * C)
    where: 2 * pi = 6.2832; f = frequency in hertz and C = capacitance in Farads
    then simple ohms law for the two series resistances will give Current and from that Power

    3183+10 = 3193 ohms

    I =V/R·· 240/3193 = 0.075 amps

    P=VI· 240*0.075 = 18W - wrong should use P=I2R here instead which gives 0.05W not 18W

    I think that's right but double check my calcs as i am rather tired at the moment cool.gif

    Post Edited (skylight) : 8/23/2008 9:10:11 PM GMT
  • stamptrolstamptrol Posts: 1,731
    edited 2008-08-23 15:38
    This sounds like the AC input card of a PLC.

    At that frequency, the impedance of the cap will dominate and appear as about 3.14K·

    That will limit current to about·76 mA. Note that your capacitor voltage rating is, IMHO, marginal for 240 VAC service.



    Cheers,

    << edit for slipped decimal>>

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    Tom Sisk

    http://www.siskconsult.com


    Post Edited (stamptrol) : 8/23/2008 9:51:56 PM GMT
  • Beau SchwabeBeau Schwabe Posts: 6,568
    edited 2008-08-23 15:48
    william chan,

    According to the simulator, the resistor will consume about 57 milli-Watts, while the capacitor will consume about 9 Watts


    www.falstad.com/circuit/

    $ 1 5.0E-6 10.20027730826997 50 5.0 50
c 176 128 304 128 0 1.0E-6 -197.6468467648667
v 176 128 176 240 0 1 50.0 240.0 0.0 0.0 0.5
g 176 240 176 304 0
r 304 128 432 128 0 10.0
g 432 128 432 304 0
o 3 64 1 35 0.15625 9.765625E-5 0 -1
o 0 64 1 35 10.0 9.765625E-5 1 -1

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    Beau Schwabe

    IC Layout Engineer
    Parallax, Inc.

    Post Edited (Beau Schwabe (Parallax)) : 8/23/2008 4:08:55 PM GMT
  • skylightskylight Posts: 1,915
    edited 2008-08-23 15:59
    Beau I cant get that link to work? you say 9W is that at 240V? I still make it 18W
  • Beau SchwabeBeau Schwabe Posts: 6,568
    edited 2008-08-23 16:11
    skylight,

    Yeah, looks like that site has poor bandwidth right now.... I just downloaded the stand-alone version (no internet required) ... www.falstad.com/circuit/circuit.zip

    Once the applet loads, go to "File" --> "Import", and then paste the code into the window .... then click "Import"

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    Beau Schwabe

    IC Layout Engineer
    Parallax, Inc.
  • skylightskylight Posts: 1,915
    edited 2008-08-23 16:23
    That sites still down but found another calculator here:

    http://www.opamplabs.com/rfc.htm

    1uf at 50 Hz comes out at 3183 ohms as in my post above, adding the 10 ohms,with ohms law this comes out at 18watts total power


    Post Edited (skylight) : 8/23/2008 4:28:41 PM GMT
  • PJAllenPJAllen Banned Posts: 5,065
    edited 2008-08-23 16:51
    The reactance and the resistance are not simply added together: Z2 = R2 + X2

    Z = (R2 + X2)1/2

    Post Edit -- Here's a better calculator: http://pr.erau.edu/~newmana/imped.html

    The answer is Z = 3183Ω


    Post Edited (PJ Allen) : 8/23/2008 4:58:59 PM GMT
  • skylightskylight Posts: 1,915
    edited 2008-08-23 16:58
    Xc already gives you the Z or impedance, the resistor can be treated as pure resistance therefore you can just add them together Z+R.

    the AC reactance part of the circuit is taken care of with the Xc formula.

    ·
  • PJAllenPJAllen Banned Posts: 5,065
    edited 2008-08-23 17:00
    skylight said...
    Xc already gives you the Z or impedance, the resistor can be treated as pure resistance therefore you can just add them together Z+R.
    No, you're wrong.
  • skylightskylight Posts: 1,915
    edited 2008-08-23 17:06
    I will have to disagree with you then as that is how i was taught at college when doing power calculations using capacitive reactance values aswell as inductive reactance values, Remember impedance·is·resistance equivalent·in ohms·in an AC circuit.
  • PJAllenPJAllen Banned Posts: 5,065
    edited 2008-08-23 17:12
    Disagree till Doomsday.· I gave the exact equation, there's no reasonable contrary position.
    ·
  • skylightskylight Posts: 1,915
    edited 2008-08-23 17:32
    Ok Pj what is X in your formula?

    I know you are going to say X= XL-Xc

    Where is the inductance in the circuit? we are talking a capacitor and resistor here no coils or such (unless you are talking of minute inductance in practice that the resistor may show, if so then if we were talking about uA it may make a difference but at the magnitudes we are discussing its negligible and can be ignored).
  • PJAllenPJAllen Banned Posts: 5,065
    edited 2008-08-23 17:41
    Sorry, skylight, I make no such contention, purely R & C as presented.·

    The impedance of an RC circuit is not the arithmetic sum of the capacitive reactance and resistance.· Why?· Because it's a reactive circuit, all of it, the R and the C, the R and the XC.

    You ought to take a look at the old texts or do some research ("wiki that.")
  • skylightskylight Posts: 1,915
    edited 2008-08-23 17:51
    Ok lets take the values and put them in the formula then and see what comes out:

    Z=sqrt ((10*10)+(3183*3183))

    Z=sqrt (100)+(10131489)

    Z=sqrt (10131589)

    Z= 3183.0157084123854508841679646369 ohms

    back where we started there is no inductance to worry about in this circuit so XL was ignored the formula above cancels out the squaring and square rooting so the resistance and reactance add together as i said before to give Z or impedance.

    I agree if the inductance in the circuit was of significance then the formula above would come into play but not in this instance.
  • PJAllenPJAllen Banned Posts: 5,065
    edited 2008-08-23 18:03
    skylight said...
    Xc already gives you the Z or impedance, the resistor can be treated as pure resistance therefore you can just add them together Z+R... that is how i was taught at college...
    That the·10Ω is not significant does not validate your arguing.· Your contention·that R and XC (or "Z" and "R" as you see it) are·simply added together·was wrong and it still is.
  • william chanwilliam chan Posts: 1,326
    edited 2008-08-23 19:32
    Skylight calculated 18w.

    Beau calculated 9.057w.

    If the capacitor is dissipating 9w, it would have been very hot after a while, but it is cool.
    I think a joule meter would show a value less than 3w.
    The reading from an actual joule meter is what is important to me.

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  • skylightskylight Posts: 1,915
    edited 2008-08-23 19:40
    You misunderstand what i was saying, the 10 ohms was included in the calculation the only reference about it was the miniscule inductance that it may contain so i treated it as purely resistive yet i still included it in the calculation.
    its the reactive element the Xc which you were saying cannot be added to the 10 ohm resistance and i was arguing the point that as there is no inductance in the circuit to react·the Z formula you were quoting takes X which is actually XL-Xc as just being Xc and therefore Z can be taken as being Xc.
    the above calculation proved it by not altering the Xc value of 3183 ohms,so·for this application the Z formula is simplified to Z=Xc.

    Maybe the difference comes from two different backgrounds where you are arguing from an electronics viewpoint and i am from a power viewpoint as an electrician. the small inductance in an RC network would make a difference if say it was a filter in a preamp for instance where uAmp/mA currents flow and those tiny inductive elements·may well be·of importance, but the OP was talking of a mains circuit with higher voltages and currents where small is meaningless and for all intents and purposes can be ignored.
  • william chanwilliam chan Posts: 1,326
    edited 2008-08-23 19:48
    Skylight,

    The calculation of the power is not simply P=VI because the voltage and current phases have been skewed by the reactive circuit.

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  • PJAllenPJAllen Banned Posts: 5,065
    edited 2008-08-23 19:52
    The Apparent Power is E * I, the actual power is ER / I.· The Power Factor (PF) =·I2R / EI =·R / Z.· The R = 10Ω, the Z = 3183Ω, therefore PF = 0.003 (0.3%)

    ·
  • william chanwilliam chan Posts: 1,326
    edited 2008-08-23 19:59
    PJ,

    In your opinion, what would be the joule meter reading?

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  • PJAllenPJAllen Banned Posts: 5,065
    edited 2008-08-23 20:02
    1 joule = 1W per sec
    Less than 1 joule.
  • william chanwilliam chan Posts: 1,326
    edited 2008-08-23 20:03
    You mean less than 1 watt?

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  • PJAllenPJAllen Banned Posts: 5,065
    edited 2008-08-23 20:06
    Affirmative.
  • william chanwilliam chan Posts: 1,326
    edited 2008-08-23 20:09
    Is it 0.003 x 18 = 54 milliwatts?

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  • skylightskylight Posts: 1,915
    edited 2008-08-23 20:43
    william chan said...
    Skylight,

    The calculation of the power is not simply P=VI because the voltage and current phases have been skewed by the reactive circuit.

    oops fell into the trap of using P=VI instead of P=I2 R for the last bit of the calculation which equals 0.05W not 18W.
    ·did say i was tired·smile.gif


    Post Edited (skylight) : 8/23/2008 9:10:54 PM GMT
  • Beau SchwabeBeau Schwabe Posts: 6,568
    edited 2008-08-23 21:09
    I think most of the confusion with this is in the difference between AC and DC circuits and how the formulas differ.

    The values that I gave rely purely on the simulator.... 10 Ohms, 1uF,·240V, ·50 Hz



    This may shed some light...

    http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/powerac.html

    http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/acres.html#c2

    "...Since the voltage and current are both sinusoidal, the power expression can be expressed in terms of the squares of sine or cosine functions, and the average of a sine or cosine squared over a whole period is = 1/2..."










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    Beau Schwabe

    IC Layout Engineer
    Parallax, Inc.

    Post Edited (Beau Schwabe (Parallax)) : 8/23/2008 9:15:53 PM GMT
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