Maximum Power Transfer Theorem (Calculus Version)

In this video, I explain the maximum power transfer theorem (MPTT) for DC electrical circuitsand prove it using calculus. Basically, you derive an equation for the load power and then take the first derivative of that with respect to the load voltage, set the first derivative to 0 and then solve for load resistance. A full proof would also require checking if that point is a local maximum or minimum, but I'll leave that part to you calculus fanatics out there. If you'd prefer a non-calculus explanation, I have a video for that too.
Basically, the MPTT describes the condition needed for the maximum power to pass from a voltage source to a load (spoiler alert, it's when the load resistor matches the source resistor)
Video Timeline
00:14 - MPTT OVerview
00:35 - Power with RL = 0
00:50 - Power with RL at infinite
01:45 - Load Power Equation
03:25 - Calculus Intro
03:50 - The Quotient rule
04:34 - Using the Quotient Rule to calculate derivative of load power equation
06:20 - Set derivative to 0 and solver for RL
08:25 - Maximum power is when RL = RS
08:30 - the Maximum Power Transfer Theorem
09:15 - "I shoulda just stopped it"
www.electronx.ca

[@tomstrum6259]

Love intuitive Electronics & have no Clue 'bout the Exotic math used Here...Can't Imagine the daily hourly Hell having to figure this Professionally every day.....Today, just run a free App calculator & spend time on Important stuff.....

[@_jmeg_3436]

Bop bop bop! 🥁 😀

[@ElectronXLab]

😀