00:01
All right, so let's say we have a battery with an internal resistance connected to a variable resistor like this, and the battery has an emf, this resistor has resistance r, and the variable one has resistance a.
00:15
So we want to adjust the resistance so that the terminal voltage is equal to the resistance of the battery.
00:23
So the effective resistance, we'll call this r -e, is just going to be since these are in series.
00:29
It'll be r plus r and so the current in the circuit is going to be our emf divided by this total resistance and so we want the basically we want the voltage drop across the smaller resistor to be as close to zero as possible because that means the total drop elsewhere in the circuit is equal to the emf of the voltage so this is going to be i times r or alternatively e times a little r over r plus r so we want this to be zero, and so that means r needs to basically be like infinitely large for that to work.
01:08
And then in order to get the maximum current from the battery, what should the resistance be adjusted to? so if we look at the current here, we already have an expression for it.
01:17
It's our emf over r plus little r.
01:22
So if we take the derivative of i with respect to our variable resistor, this is going to be negative e over.
01:30
R plus little r squared...