Find the load resistance of the circuit shown in the figure such that the maximum power is transferred to the load resistance?

Maximum Power Transfer Theorem

According to this theorem, maximum power is transferred to the load when the load resistance (R_L) is equal to the Thevenin resistance (R_th) of the circuit as seen from the load terminals.

The power delivered to the load resistor (R_L) is given by:

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

Calculation

From the figure, 6Ω and 12Ω are in parallel.

\(R={6\times 12\over 6+12}=4Ω\)

4Ω, 3Ω and 2Ω are in series.

\(R_{ab}=4+3+2=9\Omega\)