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Math Help - Why does X/XA square root become square root of XR Ohms calculation

  1. #1
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    Why does X/XA square root become square root of XR Ohms calculation

    While explaining Ohms law to someone I realised I did not understand why becomes


    I know , using practical numbers but I do not know how to prove it
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    Last edited by TeslaCoil; June 23rd 2012 at 06:23 AM. Reason: Picture ofmcalc did not show
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    Re: Why does X/XA square root become square root of XR Ohms calculation

    Quote Originally Posted by TeslaCoil View Post
    While explaining Ohms law to someone I realised I did not understand why becomes
    I know , using practical numbers but I do not know how to prove it
    \sqrt {\frac{P}{R}}  = \frac{{\sqrt {PR} }}{R}

    Thus \frac{P}{{\sqrt {PR} /R}} = \frac{{PR}}{{\sqrt {PR} }} = \sqrt {PR}
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    Re: Why does X/XA square root become square root of XR Ohms calculation

    Your "E" is usually written as "U".

    You know E=\frac{P}{\sqrt{\frac{P}{R}}}? In this case, the derivation is simple and can be done like this:

    E=\frac{P}{\sqrt{\frac{P}{R}}} = \frac{P}{\frac{\sqrt{P}}{\sqrt{R}}} = \frac{P \sqrt{R}}{\sqrt{P}} = \frac{\sqrt{P}\sqrt{P} \sqrt{R}}{\sqrt{P}} = \sqrt{P}\sqrt{R}=\sqrt{PR}


    Edit: Too slow.
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    Re: Why does X/XA square root become square root of XR Ohms calculation

    Hello, TeslaCoil!

    \text{Why does }\,\frac{P}{\sqrt{\frac{P}{R}}} \;=\;\sqrt{PR}\,?

    Can you handle fractional exponents?

    \frac{P}{\sqrt{\frac{P}{R}}} \;=\;\frac{P}{\left(\frac{P}{R}\right)^{\frac{1}{2  }}} \;=\;\frac{P}{\frac{P^{\frac{1}{2}}}{R^\frac{1}{2}  }}} \;=\;P\cdot\frac{R^{\frac{1}{2}}}{P^{\frac{1}{2}}} \;=\;P^{\frac{1}{2}}\cdot R^{\frac{1}{2}} \;=\; (PR)^{\frac{1}{2}} \;=\;\sqrt{PR}

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    Re: Why does X/XA square root become square root of XR Ohms calculation

    Thanks very much and yes! I do remember doing exponents ( 1980's)
    I am OK with the explanation except where the fourth expression inverts P&R - why does that work . I am OK with the fifth , sixth and seventh expressions

    How does every one put mathematical symbols in here? Math pad and cut and past ?
    BTW I was in Lexington MA. last October -nice area
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    Smile Re: Why does X/XA square root become square root of XR Ohms calculation

    Thank you
    I was OK with the explanation until the R &P expressions were inverted - how does that work ... using practical figure I see it does but why

    Sorry for using E instead of the SI unit V but the old "ohms magic circle" I was using for my friend showed E as ( energy) for volts and I did not want to confuse him at this point
    The blind leading the blind comes to mind
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