Determine the value of maximum power:

Determine the value of load resistance, R_L for which the source shall transfer the maximum power. Also determine the value of maximum power.

Solution

Primary we apply the Thevenin theorem and draw the Thevenin's equivalent circuit. Eliminate the load resistance RL.

Calculation for V_TH :

V_TH = Open circuit voltage across load terminals AB, and

         = V_AB

V_AB  = V_TH

= - 5 + 4 i

=- 5 + 4 ( 10/6)

= 1.66 Volt

Calculation for R_TH :

Replace all of the sources by internal resistance. (Internal resistance of ideal voltage source is zero)

R_TH       = R_AB

= 2 // 4 + 6

= (2 × 4 )/(2 + 4) + 6

= 7.33 Ω

Thevenin's Equivalent Circuit

According to maximum power transfer theorem

R_L  = R_TH = 7.33 Ω

i_L = 1.66 / (7.33 + 7.33) = 0.1132 Amp

Maximum power      P_max =( i _L )² × R_L

= 0.09398 Watts

= 93.98 m Watts