Question

Maximum Power Transfer

Learning Goal:

To find the load resistance and load power for the maximum power transferred to a load.

A resistive network containing independent and dependent sources can be modeled with a Thévenin equivalent circuit, as shown below. Maximum power transfer occurs when the load resistance RLequals the Thévenin resistance RTh

Part A

Find the Thévenin equivalent circuit with respect to the terminals a,b for the circuit above. What is the Thévenin voltage VTh?

Express your answer in V to three significant figures.

Part B

Find the load resistance RL that enables the circuit above to deliver maximum power to the terminals a,b.

Express your answer in ? to three significant figures.

Part C

Find the maximum power delivered to RL in the circuit above.

Express your answer in W to three significant figures.

Answer 1

Part A: Consider the circuit diagram 60V 6A Open circuit the load terminals. 5Ω 60 V 6A Apply KCL at node 1 5Ω 5 S2 160 5Ω From the circuit vv 03 Apply KCL at node 2. v, v,-60V 1,- 5.0 5.0 5Ω 1,11 60 Solve equations(1) and (2) gives, หุ่ = 52.5 V and 12-37.5 V So thevenin voltage is, v,,-v, 52.500 V Part B Find the Norton equivalent current to find the thevenin resistance. Short circuit the load terminals. 52 so25Ω 1 60 V SC Apply KCL at node 1 -60 V 5Ω +6 A+ 5 S2 From the circuit v, =v, 60 Apply KCL at node 2. 5.0 5.0 111 60 55 5)5 But from the circuit v 0 V substitute in equation 12-20 V Substitute all values in equation (1). 6+8=14 A Find thevenin resistance. 52.5 So load resistance should be equal to Rn to get the maximum power Part C. 52.5 4(3.75) -183.75 Watt