In case of max power transfer voltage drop across R_L is:

Concept:

Maximum power transfer theorem(MPPT)

Condition for maximum power:

R_L = R_th

Maximum power across load during MPPT:

P_max = \( {(V_{th})^2 \over 4 R_{th}}\)

Where V_th = Thevenin voltage

R_th = Equivalent resistance from load terminal or Thevenin's resistance

Calculation:

During MPPT:

RL = Rth

So, the modified diagram is given below:

Applying voltage division rule across R_L:

\(V_L = V\times {R_L \over R_L+2}\)

\(V_L = 5\times {2\over 2+2}\)

V_L = 2.5 volts

Shortcut Trick  During MPPT voltage across the load is always half the value of the supply voltage.

\(V_L= {V_S \over 2}\)

\(V_L= {5\over 2}\)

V_L = 2.5 volts