When the impedance of a load connected to a power source is varied from open-circuit to short-circuit, the power absorbed by the load has a maximum value at a load impedance which is dependent on the impedance of the power source.
Note that power is zero for an open-circuit (zero current) and for a short-circuit (zero voltage).
Voltage SourceWhen a load resistance RT is connected to a voltage source ES with series resistance RS, maximum power transfer to the load occurs when RT is equal to RS.
Under maximum power transfer conditions, the load resistance RT, load voltage VT, load current IT and load power PT are:RT = RSVT = ES / 2IT = VT / RT = ES / 2RSPT = VT2 / RT = ES2 / 4RS
Current SourceWhen a load conductance GT is connected to a current source IS with shunt conductance GS, maximum power transfer to the load occurs when GT is equal to GS.
Under maximum power transfer conditions, the load conductance GT, load current IT, load voltage VT and load power PT are:GT = GSIT = IS / 2VT = IT / GT = IS / 2GSPT = IT2 / GT = IS2 / 4GS
Complex ImpedancesWhen a load impedance ZT (comprising variable resistance RT and variable reactance XT) is connected to an alternating voltage source ES with series impedance ZS (comprising resistance RS and reactance XS), maximum power transfer to the load occurs when ZT is equal to ZS* (the complex conjugate of ZS) such that RT and RS are equal and XT and XS are equal in magnitude but of opposite sign (one inductive and the other capacitive).
When a load impedance ZT (comprising variable resistance RT and constant reactance XT) is connected to an alternating voltage source ES with series impedance ZS (comprising resistance RS and reactance XS), maximum power transfer to the load occurs when RT is equal to the magnitude of the impedance comprising ZS in series with XT:RT = ZS + XT = (RS2 + (XS + XT)2)1÷2Note that if XT is zero, maximum power transfer occurs when RT is equal to the magnitude of ZS:RT = ZS = (RS2 + XS2)1÷2
When a load impedance ZT with variable magnitude and constant phase angle (constant power factor) is connected to an alternating voltage source ES with series impedance ZS, maximum power transfer to the load occurs when the magnitude of ZT is equal to the magnitude of ZS:(RT2 + XT2)1÷2 = ZT = ZS = (RS2 + XS2)1÷2
Note that power is zero for an open-circuit (zero current) and for a short-circuit (zero voltage).
Voltage SourceWhen a load resistance RT is connected to a voltage source ES with series resistance RS, maximum power transfer to the load occurs when RT is equal to RS.
Under maximum power transfer conditions, the load resistance RT, load voltage VT, load current IT and load power PT are:RT = RSVT = ES / 2IT = VT / RT = ES / 2RSPT = VT2 / RT = ES2 / 4RS
Current SourceWhen a load conductance GT is connected to a current source IS with shunt conductance GS, maximum power transfer to the load occurs when GT is equal to GS.
Under maximum power transfer conditions, the load conductance GT, load current IT, load voltage VT and load power PT are:GT = GSIT = IS / 2VT = IT / GT = IS / 2GSPT = IT2 / GT = IS2 / 4GS
Complex ImpedancesWhen a load impedance ZT (comprising variable resistance RT and variable reactance XT) is connected to an alternating voltage source ES with series impedance ZS (comprising resistance RS and reactance XS), maximum power transfer to the load occurs when ZT is equal to ZS* (the complex conjugate of ZS) such that RT and RS are equal and XT and XS are equal in magnitude but of opposite sign (one inductive and the other capacitive).
When a load impedance ZT (comprising variable resistance RT and constant reactance XT) is connected to an alternating voltage source ES with series impedance ZS (comprising resistance RS and reactance XS), maximum power transfer to the load occurs when RT is equal to the magnitude of the impedance comprising ZS in series with XT:RT = ZS + XT = (RS2 + (XS + XT)2)1÷2Note that if XT is zero, maximum power transfer occurs when RT is equal to the magnitude of ZS:RT = ZS = (RS2 + XS2)1÷2
When a load impedance ZT with variable magnitude and constant phase angle (constant power factor) is connected to an alternating voltage source ES with series impedance ZS, maximum power transfer to the load occurs when the magnitude of ZT is equal to the magnitude of ZS:(RT2 + XT2)1÷2 = ZT = ZS = (RS2 + XS2)1÷2
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