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?

 

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

 

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?