Maximum power is transferred when

According to the maximum power transfer theorem, to obtain maximum power from external power from a source with finite impedance, the impedance of the load must be equal to source impedance.

Derivation:

From the above circuit, the current flowing through the load, ‘I’ is given as

Power transferred to the load,

In the above equation, RL is a variable, therefore the condition for maximum power delivered to the load is determined by differentiating load power with respect to the load resistance and equating it to zero.

→ (RL + RTH)2 = 2RL (RTH + RL)

→ RL + RTH = 2RL

→ RL = RTH