The maximum power transfer theorem states that to obtain maximum external power from a power source with internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals.
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But here, we are asked to find the value of R, and not RL that will result in the maximum power to be transferred to load RL. So we cannot go by the standard procedure of equating RL with the Thevenin equivalent resistance.
Maximum power transfer theorem states that " In a linear bilateral network if the entire network is represented by its Thevenin's equivalent circuit then the maximum power transferred from source to the load when the load impedance is equal to the complex conjugate of Thevenin's impedance".
The maximum power transfer theorem states that the maximum power flow through an AC circuit will occur when the load impedance is equal to the complex conjugate of the source impedance.
The maximum power theorem, better known as the maximum power transfer theorem, is an essential tool for ensuring successful system design. Put simply, this theorem states that the maximum power that can be transferred from source to load is 50%, which occurs when source impedance is exactly matched to load impedance. The theorem is not as simple as it seems at first glance, however, and can be easily misunderstood.
It was Thomas Edison who realized maximum power transfer and maximum efficiency are different entities. If load resistance is increased, higher efficiency can be achieved. Efficiency is the percentage of input power that is dissipated in the load. The maximum power transfer theorem tells us the load resistance, which will get maximum magnitude of power delivered to it by the source. However, input power from the source depends on load; if load resistance is increased, overall power decreases in magnitude, but the percentage of input power transferred to load increases. In other words, when load resistance increases, more power is dissipated in the load than in the source impedance, Hence, efficiency is increased. The magnitude of overall power is decreased, however, due to the increased resistance. Similarly, if load resistance is decreased, a lower percentage of total input power is dissipated in the load, and efficiency decreases.
For day-to-day applications, this is useful when the maximum possible magnitude of power must be transferred from a fixed source. For systems in which input voltage does not normally change and maximum power transfer is required, achieving maximum efficiency is not important. For example, the impedance of an amplifier is matched to a loudspeaker to gain maximum power transfer and, thus, maximum volume of sound.
While accurate, balanced impedance matching can lead to the desired maximum power transfer in some instances, an unmatched system can lead to loss. Excessive power loss, heat dissipation, and even circuit failure can all result from improper impedance matching. In these cases, reduced efficiency is a result of improper matching, which causes excessive power loss.
Impedance matching transformers are designed to provide maximum power transfer from source to load, altering circuit impedances to allow for necessary matching. By applying an appropriate turns ratio to the ratio of load impedance to output impedance, these devices translate resistance on one side of the circuit into the required value on the other side.
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Here is a graph which clearly shows that maximum power transfer occurs when Rth=RL.if(typeof ez_ad_units != 'undefined')ez_ad_units.push([[250,250],'electricalacademia_com-large-mobile-banner-1','ezslot_10',113,'0','0']);__ez_fad_position('div-gpt-ad-electricalacademia_com-large-mobile-banner-1-0');
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