Consider a DC voltage source connected to a load resistance in the circuit diagram below.

efficient-power-transfer-1.png

It is easy to work out the power dissipated in the resistor:

P = V x I

I = V / R

P = V2 / R

P = I2 R

What happens to the power dissipated as the load resistance R approaches 0 ohms? The current approaches an infinite value, and the power dissipated approaches an infinite value! In the real world, it is not possible to build a DC voltage source that can supply infinite power and there are no connecting wires that can handle an infinite current. The DC voltage source itself will include some "internal resistance". This is represented by R1 in the circuit diagram below.

efficient-power-transfer-1.png

With the knowledge that the voltage generator has internal resistance R1, the question can be asked once again. What happens to the power dissipated as the load resistance R2 approaches 0 ohms? This time we have a voltage source of Vgen supplying current to the internal resistance of the DC voltage source (R1), so the power supplied is given by:

P = Vgen2 / R1

This is an interesting result: all of the power is dissipated in R1, so the DC voltage source itself will warm up, and no power is supplied anywhere else. Once again in the real world the connecting wiring will have a very small resistance and will dissipate some power but this can be assumed to be negligably small in comparison to that dissipated by R1. When the load resistance R2is not 0 Ohms, the total power dissipated by R1 and R2 is given by:

P = Vgen2 / (R1 + R2)

It is then also easy to calculate the power dissipated by R1 and R2 individually:

I = V / R

I = Vgen / (R1 + R2)

PR1 = (Vgen / (R1 + R2))2 R1

PR2 = (Vgen / (R1 + R2))2 R2

Now the power dissipated in the load PR2 can be compared to the power dissipated in the DC voltage source internal resistance PR1:

PR2 / PR1 = R2 / R1

This is another interesting conclusion, and can be expressed in words as follows:

To efficiently transfer power from a power supply to a load it is important to ensure that the load resistance is high in comparison to the power supply internal resistance.

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