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Maximum power transfer
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Load equal to source resistance gives maximum power.
R_L = rA load draws the most power from a source when its resistance equals the source's internal resistance: R_L = r, giving P_max = ε²/4r with only 50% efficiency.
ε = 12 V, r = 2 Ω: 18 W.
Power stations aim for high efficiency instead.
In more detail
Maximum power is transferred to a load when its resistance equals the internal resistance of the source. The power delivered then is EMF squared divided by four times the internal resistance.
Real-world uses
- Audio amplifiers are matched to speakers for maximum power output.
- Radio transmitters match antennas to their output impedance.
- Audio engineers match the load impedance to the amplifier so that the maximum power is delivered to the speaker.
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Frequently asked questions
Is maximum power the same as maximum efficiency?
No. At maximum power, the efficiency is only 50%.
Why matching?
It ensures the source delivers its power to the load rather than wasting it internally.
Is maximum power the same as maximum efficiency?
No. Maximum power transfer occurs when the load equals the source resistance, but at that point half the power is wasted in the source.
Related topics in Current Electricity & Circuits
Ammeter and voltmeter · Galvanometer · Multimeter · Thevenin's theorem · Norton's theorem · Superposition theorem