# Maximum Power Transfer Theorem

Moritz von Jacobi introduced Maximum Power Transfer Theorem in the year 1840. The theorem establishes a condition between the power source and the load.  At that condition, a power source can deliver the maximum power to the load.

## Statement of Maximum Power Transfer Theorem

“A power source can deliver maximum power to the load connected to it when the resistance of the load is equal to the resistance of the source.”

### Applications of Maximum Power Transfer Theorem

We can apply Maximum Power Transfer Theorem to both AC and DC circuits. The AC circuits may be with reactance as well. In AC circuits the maximum power transfer occurs when load impedance equals complex conjugate of the source impedance.

### Explanation of Maximum Power Transfer Theorem

To simplify this, let us connect a power source with internal resistance Rs to a load of resistance RL as shown below: Hence, on the basis of the above circuit diagram, the power delivered to the connected load will be, In order to find the condition for maximum power transfer, we have to differentiate equation (i) w.r.t RL and further equate the differentiated equation to zero. On differentiating equation (i), we get, After differentiating equation (i) and equating it to zero, we get, RL = RS

This is the required condition. Thus, to transfer maximum power from the source to load, the resistance of connected load must equal to the resistance of the source. Further, the following conditions can be established.

#### Different Conditions of Power Transfers

Rs = RL

When the resistance of the source equals the resistance of load results in maximum power transfer to load from the source. This is the actual condition of Maximum Power Transfer Theorem.

Rs > RL

When the source resistance is greater than the load resistance results in power dissipation in the source. Here, the overall resistance of the circuit is low and that results in overall high power dissipation but the power transferred to the load is low.

Rs < RL

When the resistance of the load is greater than the resistance of the source results in higher overall resistance of the circuit and that reduces the magnitude of the power transferred to the load although a greater fraction of the total power is transferred to the load.

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