My Math Forum Joules into a load

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 September 29th, 2014, 11:44 PM #1 Senior Member   Joined: Apr 2014 From: UK Posts: 917 Thanks: 331 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?
 September 29th, 2014, 11:53 PM #2 Senior Member   Joined: Apr 2014 From: UK Posts: 917 Thanks: 331 After further though, is it more like: integrate[0 to 2] (400-200x)^2 /1.2 dx ?
 September 30th, 2014, 06:54 AM #3 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,156 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions 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.
 October 1st, 2014, 12:17 AM #4 Senior Member   Joined: Apr 2014 From: UK Posts: 917 Thanks: 331 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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