Maximum power transfer occurs when the load voltage and current are: 

Maximum Power Transfer Theorem

The maximum power transfer theorem states that the maximum power is delivered to a load when the load resistance is equal to the source resistance.

The maximum power across the load is given by:

 \(P_{max}={V_{th}^2\over 4R_{th}}\)

Calculation

When maximum power flows from source to load, the voltage across the load is half of the Thevenin voltage.

Consider Thevenin voltage = V_th

The voltage across the load, \(V_L={V_{th}\over 2}\)

The current drawn from the source is given by:

\(I={V_{th}- {V_{th}\over 2}\over R}\)

\(I=\rm \frac{V_{th}}{2R}\)