Question

In the circuit shown in Fig. obtain the condition from maximum power transfer to the load R_L. Hence determine the maximum power transferred.

Answer 1

We will find Thevenin’s equivalent circuit to the left of trminals A and B for which purpose we will convert the battery source into a current source as shown in Fig. 

By combining the two current sources, we get the circuit of Fig.  It would be seen that open circuit voltage V_AB equals the drop over 3Ω resistance because there is no drop on the 5Ω resistance connected to terminal A.

Now, there are two parallel path across the current source each of resistance 5 Ω. Hence, current through 3 Ω resistance equals 1.5/2 = 0.75 A. 

Therefore, V_AB = V_th = 3 × 0.75 = 2.25 V with point A positive with respect to point B. For finding R_AB, current source is replaced by an infinite resistance. 

∴ R_AB = R_th = 5 + 3 || (2 + 5) = 7.1 Ω 

The Thevenin’s equivalent circuit along with R_L is shown in Fig.  As per, the condition for MPT is that 

R_L = 7.1 Ω. 

Maximum power transferred = V_th²/4R_L = 2.252/4 × 7.1 = 0.178W = 178mW