A number of observations can be made on a practical voltage source and its load resistor. The voltage across the load can be calculated with voltage division and the current can be calculated with Ohm's law.
$ V_l = V_0 ⋅ \dfrac{R_l}{R_i + R_l} $
$ I = \dfrac{V_0}{R_i + R_l} $
Efficiency is the ratio of useful and total power. In the series circuit above, because current is common, it can be calculated with voltages instead, and using the formula above, efficiency becomes the ratio of resistances. As the load increases, efficiency also increases, as more voltage falls across the high load, less falls across the internal resistor. Thus the ratio becomes higher.
$ \mu_l = \dfrac{P_l}{P_0} = \dfrac{V_l}{V_0} = \dfrac{R_l}{R_i + R_l} $
Power is the product of voltage and current. Unlike the efficiency, the power output curve does not increase in a strict monotonic fashion, but first increases and then slowly decreases as the load increases. This means that there is a load point at which the maximum possible power can be extracted from a voltage source.
$ P_l = V_l ⋅ I = \dfrac{V_0^2 ⋅ R_l}{(R_i + R_l)^2} $
The maximum position of the power curve is exactly the same as the internal resistance. This means that the maximum possible power can be drawn from a power source when the load resistance is the same as the internal resistance of the generator. By plotting the power against the efficiency curve, it is clear that the efficiency is only 50% at maximum power. Better efficiency can be achieved at the expense of power.
$ R_l = R_i $
$ P_{max} = \dfrac{V_0^2}{4 ⋅ R_i} $
Matching impedance (AC resistance) is an essential design step in many areas, whether it's maximising the power transferred between the phone and the charger in a wireless charger, between amplifiers and speakers, or between the antenna, the signal transmission line (e.g. coax cable) and the transmitter/receiver in radio frequency (RF) and microwave systems.
Another example is the MPPT type solar charge controller. Their task is to follow the highest power point and load the panel accordingly, so that there is less loss and the connected battery charges faster. The V-I curves of solar panels decrease slowly at first and then suddenly drops, and the amount of current depends on the strength of the solar radiation. The MPP is somewhere at the beginning of the current drop.