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Consider a very simple series circuit consisting of a battery with an open circuit voltage of Vs (voltage source), a battery internal resistance of Ri, and a load resistor Rl.
The load current is Vs / (Ri + Rl).
The load voltage is Vl = Vs*Rl / (Ri + Rl)
In this circuit the load power is the power dissipated in the load resistor. This is I^2*R or I*V.
Using the load voltage and current you get
Pl = Vs*Vs*Rl / (Ri + Rl)^2
The power loss in this circuit is the power dissipated in the internal resistance. The internal resistance is of no use relative to the load and therefore classified as a loss.
If Ri is constant and you vary Rl, then what is the value of Rl that produces the maximum power dissipation in the load resistor, and what is the amount of power supplied by the battery under this maximum power transfer condition?
Would operation of a power distribution system be a good design if operated at this maximum load power point?
Consider some actual numbers.
Vs = 6
Ri = 1
Rl = 5
The power supplied from the source is 6*1 = 6 W
Pl = 36*5 / 6^2 = 36*5 / 36 = 5 W
Pi = 36*1 / 36 = 1 W
Does this help?
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