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A purely resistive Thevenin source transfers maximum load power when load and source resistance match.
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Formula
RL and RTh in Ω
| Symbol | Meaning | Unit |
|---|---|---|
| Ohmic load resistance | Ω | |
| Thevenin source resistance | Ω |
R_L=R_{Th}This condition maximizes power delivered to RL in a fixed linear DC Thevenin model. Half of source power is dissipated internally at this point, so efficiency is not maximized. AC matching uses complex conjugate impedance under different conditions.
This condition maximizes power delivered to RL in a fixed linear DC Thevenin model. Half of source power is dissipated internally at this point, so efficiency is not maximized. AC matching uses complex conjugate impedance under different conditions.
A purely resistive Thevenin source transfers maximum load power when load and source resistance match.
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Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Load resistance for maximum power transfer” and check its unit and magnitude.
A source with RTh=50 Ω delivers maximum load power at RL=50 Ω.
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Use variable definitions and check: RL and RTh in Ω.
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A purely resistive Thevenin source transfers maximum load power when load and source resistance match.
A source with RTh=50 Ω delivers maximum load power at RL=50 Ω.
Understand load matching in linear sources and measurement circuits.
Here is how to work through a typical Load resistance for maximum power transfer (RL = RTh) task step by step:
Task
Work through the numerical example for “Load resistance for maximum power transfer” and check its unit and magnitude.
Solution path
A source with RTh=50 Ω delivers maximum load power at RL=50 Ω.
Load power is P=UTh2RL/(RTh+RL)2. Differentiating with respect to RL gives a maximum at equality. Very small loads have low voltage; very large loads have low current, so the product peaks between them. This maximizes resistive load power, not efficiency; AC matching uses a complex condition. Application: Understand load matching in linear sources and measurement circuits. The numerical example A source with RTh=50 Ω delivers maximum load power at RL=50 Ω anchors the idea in a concrete measurement case. The corresponding units are RL and RTh in Ω. A source with RTh=50 Ω delivers maximum load power at RL=50 Ω. This checks that the reference quantities are compatible.
No. At RL=RTh, equal power is dissipated internally and in the load in the ideal model, so source-to-load efficiency is 50%. Power systems often choose another point to reduce losses. This maximizes resistive load power, not efficiency; AC matching uses a complex condition. The corresponding units are RL and RTh in Ω. A source with RTh=50 Ω delivers maximum load power at RL=50 Ω. This checks that the reference quantities are compatible. Scope: This condition maximizes power delivered to RL in a fixed linear DC Thevenin model. Half of source power is dissipated internally at this point, so efficiency is not maximized. AC matching uses complex conjugate impedance under different conditions. A practical application is Understand load matching in linear sources and measurement circuits.
For a linear AC source, maximum average load power generally uses a load impedance conjugate to source impedance. Equality of real resistances is the DC or purely resistive special case. This maximizes resistive load power, not efficiency; AC matching uses a complex condition. Scope: This condition maximizes power delivered to RL in a fixed linear DC Thevenin model. Half of source power is dissipated internally at this point, so efficiency is not maximized. AC matching uses complex conjugate impedance under different conditions. A practical application is Understand load matching in linear sources and measurement circuits.
Write the quantity and unit from the variable list next to every value: RL and RTh in Ω. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example A source with RTh=50 Ω delivers maximum load power at RL=50 Ω. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. This maximizes resistive load power, not efficiency; AC matching uses a complex condition.
The background states this starting condition: This condition maximizes power delivered to RL in a fixed linear DC Thevenin model. Half of source power. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. This maximizes resistive load power, not efficiency; AC matching uses a complex condition.
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