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Change in watts and power dissipated

  1. May 26, 2013 #1
    One of my homework questions is giving me trouble:

    "In, the US, the rms voltage from power outlets (known as line voltage) is 120 V. In the United Kingdom, line voltage is 230 V. If you take a lamp with a standard 100 W incandescent light bulb from the US, how much power will it dissipate if used in the UK? Assume that the electrical resistance of the bulb is constant."


    So, I know that V=IR and P=VI. V1=120 V and V2= 230 V and the P of the light bulb= 100 W. Should I plug in power of the light bulb to the formula P=IV and find the current and then use that to find the excess power. For example,

    P/V=I

    (100W)/(120V)=I

    I=0.8A

    P=(0.8A)(230 V)= 200 W - 100 W = 100 W dissipated

    I have no idea if I am on the right track or not, please help.

    Thanks in advance.
     
  2. jcsd
  3. May 26, 2013 #2

    OmCheeto

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    Gold Member
    2016 Award

    bolding mine

    No. Find the resistance of the lightbulb. As stated; "Assume that the electrical resistance of the bulb is constant."
    You are welcome.
     
  4. May 26, 2013 #3
    So, should I calculate it like this:

    P/V=I

    (100W)/(120V)=I

    I=0.83A

    R=V/I = 120V/0.83A = 145 Ω

    R=100 Ω

    and then would I use the formula P=I^2*R ?
     
  5. May 26, 2013 #4

    gneill

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    Staff: Mentor

    There's another power relation that might prove to be helpful: P = V2/R.
     
  6. May 26, 2013 #5
    P/V=I
    (100W)/(120V)=I
    I=0.83A

    R=V/I = 120V/0.83A = 145 Ω
    R=100 Ω

    Then,
    P = V2/R
    P=(230V)^2/100Ω=529 W

    So,
    529W-100W = 429W or 400W dissipated?
     
  7. May 26, 2013 #6

    gneill

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    Staff: Mentor

    Why do you write R = 100 Ω after calculating it to be 145 Ω ?
    Does the question ask you to find the actual power dissipated or the difference in power dissipated? When I read the quoted question, it looks like they just want the power dissipated by that bulb when it's energized at 230V.
     
  8. May 26, 2013 #7
    Oh, oops, I was going by sig. figs. I recalculated and got 370 W dissipated.

    I thought by "dissipated" meant the extra power that isn't being used by the 100W light bulb and that is why I found the difference. Hmmm, I guess not.
     
  9. May 26, 2013 #8
    Also, thank you so much for you input!
     
  10. May 26, 2013 #9

    gneill

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    Staff: Mentor


    Your 370W value looks quite reasonable. You're welcome :smile:
     
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