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

**TeslaCoil** · June 23rd 2012, 06:20 AM

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

**Plato** · June 23rd 2012, 06:34 AM

Originally Posted by TeslaCoil

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 $\frac{P}{{\sqrt {PR} /R}} = \frac{{PR}}{{\sqrt {PR} }} = \sqrt {PR}$

**mfb** · June 23rd 2012, 06:39 AM

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.

**Soroban** · June 23rd 2012, 09:06 AM

Hello, TeslaCoil!

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

Can you handle fractional exponents?

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

**TeslaCoil** · June 23rd 2012, 10:31 PM

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

**TeslaCoil** · June 23rd 2012, 10:39 PM

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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