00:01
The two resistors, r and r, are in series.
00:06
So the equivalent resistance of the circuit is just little r plus big r, which means that the current is the emf over that equivalent resistance.
00:20
So the power delivered to the load resistors will be i squared r, which is the emf over r plus r squared times r.
00:44
Or emf squared r over r plus r squared.
00:51
Now, if we want to maximize the delivered power, well, a maxima occurs when the derivative is zero, so we want dpdr to be zero.
01:10
Well, dpdr will be epsilon squared times going through the quotient rule, r plus r squared times the derivative of r, which is one, minus the derivative of this is r times two times r plus little r, all over r plus little r to the fourth, which again is equal to zero.
01:46
Okay, let's write this a little more neatly.
01:52
I can drop my denominator because in order to get this equal to zero, the numerator is what has to be equal to zero.
02:02
So epsilon squared times r plus...