September 29th, 2014, 11:44 PM  #1 
Senior Member Joined: Apr 2014 From: UK Posts: 898 Thanks: 329  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: 898 Thanks: 329 
After further though, is it more like: integrate[0 to 2] (400200x)^2 /1.2 dx ? 
September 30th, 2014, 06:54 AM  #3 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,142 Thanks: 726 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 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: 898 Thanks: 329 
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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