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September 29th, 2014, 11:44 PM   #1
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Joules into a load

I have an energy source which when applied accross a 1.2R resistor, drops from 400V to 0V linearly over 2 seconds.
I'm trying to work out what integral equation I need to work out the Joules absorbed by the resistor, but it's not apparent to me what it should look like.
I've got as far as:
Integrate[0 to 2] 400*400/1.2 - something
I'm struggling with the something part!
Any ideas?
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September 29th, 2014, 11:53 PM   #2
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After further though, is it more like:
integrate[0 to 2] (400-200x)^2 /1.2 dx
?
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September 30th, 2014, 06:54 AM   #3
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For an Ohmic resistor,

$\displaystyle V = IR,$
$\displaystyle P = IV$

where V, I, R and P are voltage, current, resistance and power respectively. Also,

$\displaystyle E = \int^2_0 P(t) dt = \int^2_0 I(t)V(t) dt = \int^2_0 \frac{(V(t))^2}{R}dt$

where E is total energy (in Joules) and $\displaystyle V(t) = 400 - 200t$ can be used as your voltage function. It assumes 100% efficiency and a constant resistance, which are reasonable assumptions for Ohmic resistors.

I'll leave it up to you to do the rest
Thanks from topsquark and weirddave

Last edited by Benit13; September 30th, 2014 at 07:01 AM.
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October 1st, 2014, 12:17 AM   #4
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Cheers for that, it's been 15 years since I attempted this sort of thing.
If I did it right, I got 240KJ.
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