Question

In the network shown in Fig., find the value of R_L such that maximum possible power will be transferred to R_L. Find also the value of the maximum power and the power supplied by source under these conditions.

Answer 1

We will remove R_L and find the equivalent Thevenin’s source for the circuit to the left of terminals A and B. As seen from Fig.  V_th equals the drop across the vertical resistor of 3Ω because no current flows through 2 Ω and 1 Ω resistors.

 

Since 15 V drops across two series resistors of 3 Ω each, V_th = 15/2 = 7/5 V. 

Thevenin’s resistance can be found by replacing 15 V source with a short-circuit. 

As seen from Fig. , R_th = 2 + (3 || 3) + 1 = 4.5 Ω. Maximum power transfer to the load will take place when R_L = R_th = 4.5 Ω.

Maximum power drawn by R_L = V_th 2 /4 × R_L = 7.52 /4 × 4.5 = 3.125 W. 

Since same power in developed in R_th, power supplied by the source = 2 × 3.125 = 6.250W.