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

#### enesene

Joined Mar 3, 2020
21

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
614
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