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Power and Voltage

  1. Sep 6, 2004 #1
    Q20-9. The power rating of a 570 W heater specifies the power consumed when the heater is connected to an ac voltage of 120V. What is the power consumed by two of these heaters connected in series, connected to the same voltage?

    570 W
    285 W
    1140 W
    2280 W
    142.5 W

    ok, my original thinking was that the 120V will supply 570 W of power and that two in a series would still have a total power of 570W (285W each)...but that was wrong...so is it double the power (1140W)- is the power consumed still 570W for each heater- and so 1140 is the total?

    thanks
     
  2. jcsd
  3. Sep 6, 2004 #2

    chroot

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    Staff Emeritus
    Science Advisor
    Gold Member

    Power is voltage times current. Ohm's law says voltage is current times resistance.

    [tex]P = V \cdot I = \frac{V^2}{R}[/tex]

    Solving for resistance:

    [tex]R = \frac{V^2}{P}[/tex]

    Replacing R with 2R:

    [tex]P_{\textrm{both}} = \frac{V^2 \cdot P}{2 V^2} = \frac{P}{2}[/tex]

    - Warren
     
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