What's the difference between this Max. Power Transfer formulas.

Thread Starter

enesene

Joined Mar 3, 2020
17
zssad.png

both of the formulas (1 and 2) shows us total power delivered to load but they're not same? Did you know where's the mistake?
 

Delta prime

Joined Nov 15, 2019
336
No problem here you go!:)

I = VTH / ZTH + ZL



Where ZL = RL + jXL



ZTH = RTH + jXTH



Therefore, I = VTH / (RL + jXL + RTH + jXTH )



= VTH / ((RL+ RTH) + j(XL + XTH ))



The power delivered to the load,



PL = I2 RL



PL = V2TH × RL / ((RL+ RTH)2 + (XL + XTH )2) ……(1)​

For maximum power the derivative of the above equation must be zero, after simplification we get


XL + XTH = 0



XL = – XTH​

Putting the above relation in equation 1, we get


PL = V2TH × RL / ((RL+ RTH )2​

Again for maximum power transfer, derivation of above equation must be equal to zero, after simplification we get


RL+ RTH = 2 RL



RL = RTH​

Hence, the maximum power will transferred to the load from source, if RL = RTH and XL = – XTH in an AC circuit. This means that the load impedance should be equal to the complex conjugate of equivalent impedance of the circuit,


ZL = ZTH​

Where ZTH is the complex conjugate of the equivalent impedance of the circuit.


This maximum power transferred,
Pmax = V2TH / 4 RTH or V2TH/ 4 RL
 

Thread Starter

enesene

Joined Mar 3, 2020
17
Thank you for everything. According to formulas that you said, The answer is 62,5 which is same with Number 1 formula on the picture.

What about second formula? Don't we get maximum power transferred to load with √ (Active power)2 + (Reactive Power)2 formula, too?
 
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