Power transfer and impedence matching.

[duckandcover]

What is the physical explanation for the power transfer in a circuit being maximum when the resistance of the system is equal to the internal resistance?

maybe heat loss?

any help would be appreciated as i understand the mathematical proof but do not know much about the physical causes.

 

[Mapes]

If the resistance of the load $R_\mathrm{load}$ is very low (so that the current I is approximately constant through the load and independent of $R_\mathrm{load}$), then the power transfer $I^2R_\mathrm{load}$ will be small. If the resistance of the load is very high (so that the voltage V is approximately constant across the load and independent of $R_\mathrm{load}$), then the power transfer $V^2/R_\mathrm{load}$ will be small. In between these two extremes is a happy medium, specifically at $R_\mathrm{load}=R_\mathrm{source}$.

 

[nlightner]

The physical explanation for the maximum power transfer in a circuit occurs when the resistance of the system is equal to the internal resistance. This is due to the concept of impedance matching, which is the process of ensuring that the impedance of a source matches the impedance of a load. In a circuit, the source is the power supply and the load is the internal resistance of the circuit.

When the resistance of the system is equal to the internal resistance, the impedance of the circuit is matched, meaning that the energy transfer between the source and the load is at its most efficient. This is because the voltage and current in the circuit are in phase, resulting in a maximum transfer of power.

On the other hand, if the resistance of the system is not equal to the internal resistance, the impedance of the circuit is not matched. This can result in a phase difference between the voltage and current, leading to a decrease in the efficiency of power transfer. This is due to the fact that some of the energy is lost as heat due to the mismatched impedance, resulting in a decrease in the overall power transfer.

Therefore, by matching the impedance of the source and load, the circuit is able to transfer the maximum amount of power without any energy loss, making it the most efficient way to transfer power. This concept is crucial in the design and optimization of electrical circuits, as it allows for the most efficient use of energy.