Maximum Power Transfer in Case of DC Network:

Figure, illustrates the DC network for maximum power transfer. The load current is given by

iL  = V_TH / R_TH + R_L

Power delivered to load

P_L = (i_L )² × R_L   = ( (V_TH )² /(R _TH + R  )² )× R_L

Condition for maximum power

dP_L/ dR_L       = 0

⇒         R_L = R_TH

So load resistance must be equal to the internal resistance of circuit for receiving the maximum power.

The maximum power from equation

P_max  =( V_Th ) ²/(R_L+ R_L )× R_L   = V_TH /4 R_L

P _max     =          V_TH   /4 R_TH

Maximum power transfer theorem is useful in communication network and electronic circuits where demand of maximum power is important instead of the efficiency. The total efficiency of a network supplying maximum power to any branch is only 50%. So use of maximum power transfer theorem is restricted in electrical and distribution networks where aim is high efficiency not the maximum power.

As earlier stated, before applying the maximum power transfer theorem, we suppose that circuit must be in Thevenin's equivalent form. So, here we describe the Thevenin theorem and then draw the Thevenin's equivalent circuit.

Thevenin theorem states that any linear bilateral network across its load terminal may be replaced by simple network having one voltage source (V_TH) and one series impedance (Z_TH).