maximum power transfer theorem?
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In electrical engineering, the maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals. Moritz von Jacobi published the maximum power (transfer) theorem around 1840; it is also referred to as "Jacobi's law".[1]
The theorem results in maximum powertransfer across the circuit, and not maximum efficiency. If the resistance of the load is made larger than the resistance of the source, then efficiency is higher, since a higher percentage of the source power is transferred to the load, but the magnitude of the load power is lower since the total circuit resistance goes up.
If the load resistance is smaller than the source resistance, then most of the power ends up being dissipated in the source, and although the total power dissipated is higher, due to a lower total resistance, it turns out that the amount dissipated in the load is reduced.
The theorem states how to choose (so as to maximize power transfer) the load resistance, once the source resistance is given. It is a common misconception to apply the theorem in the opposite scenario. It does not say how to choose the source resistance for a given load resistance. In fact, the source resistance that maximizes power transfer is always zero, regardless of the value of the load resistance.
The theorem can be extended to alternating current circuits that include reactance, and states that maximum power transfer occurs when the load impedance is equal to the complex conjugate of the source impedance.
The theorem results in maximum powertransfer across the circuit, and not maximum efficiency. If the resistance of the load is made larger than the resistance of the source, then efficiency is higher, since a higher percentage of the source power is transferred to the load, but the magnitude of the load power is lower since the total circuit resistance goes up.
If the load resistance is smaller than the source resistance, then most of the power ends up being dissipated in the source, and although the total power dissipated is higher, due to a lower total resistance, it turns out that the amount dissipated in the load is reduced.
The theorem states how to choose (so as to maximize power transfer) the load resistance, once the source resistance is given. It is a common misconception to apply the theorem in the opposite scenario. It does not say how to choose the source resistance for a given load resistance. In fact, the source resistance that maximizes power transfer is always zero, regardless of the value of the load resistance.
The theorem can be extended to alternating current circuits that include reactance, and states that maximum power transfer occurs when the load impedance is equal to the complex conjugate of the source impedance.
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here is ur ans..◽
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Maximum power transfer theorem states that, the maximum power output from a source with finite internal resistance is obtained while the load resistance is equal to the internal resistance of the source viewed from its output terminals.
Let's take an example of a 12V batterywhich has an internal resistance of 3Ω.
If an external load of 2Ω, 3Ω, 4Ω are connected one after another. Now calculate the power delivered to the loads in each case.
Case 1:
I1 = 12V/ (3Ω+2Ω) = 2.4A
P1 = 2×(2.4)² W = 11.52W
Case 2:
I2 = 12/(3Ω+3Ω) =2A
P2 = 3Ω× 2A² = 12W
Case 3:
I3 = 12V/ (3Ω+4Ω) = 1.71A
P3 = 4Ω×(1.71A)² W = 11.628W
Maximum power is delivered when external resistance is 3Ω, which is equal to the internal resistance of the battery.
Here I have shown a simple example. You can use graphical representation also.
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