Thevenin equivalent of circuit and maximum power transfer

In summary, the Thevenin equivalent of a circuit is a simplified circuit used to represent the behavior of a more complex circuit. It consists of a single voltage source and resistor. The Thevenin equivalent can be determined by finding the open-circuit voltage and equivalent resistance. Maximum power transfer is the condition where the load receives the maximum amount of power from the source, which can be achieved by adjusting the load resistance to match the Thevenin equivalent resistance. These concepts are important in circuit analysis as they allow for the simplification and optimization of complex circuits and help determine the best load resistance for maximum power transfer.
  • #1
bizuputyi
42
1

Homework Statement



Find the Thévenin equivalent of the circuit and the required value of the load for maximum power transfer for [itex] Z = 15 + j24 Ω [/itex].

Homework Equations



Voltage divider equation and [itex] Z_{in} = Z_{load} [/itex] 'complex conjugate' for maximum power transfer.

The Attempt at a Solution



Thévenin equivalent:

Since there is no current flowing through 2.5Z:

[itex] V_{out} = V_{in} \times \frac{2 \parallel 5}{2 + (2 \parallel 5)} = 0.4167 V_{in} [/itex]

[itex] Z_{total} = 0.67Z [/itex]

Maximum power transfer:

[itex] Z_{load} = 0.67 \times (15-j24) = 10 - j16 Ω[/itex]

Does this appear to be correct?
Thank you for anyone looking into that.
 

Attachments

  • circuit.jpg
    circuit.jpg
    18 KB · Views: 462
  • thevenin equivalent.jpg
    thevenin equivalent.jpg
    7.4 KB · Views: 473
Physics news on Phys.org
  • #2
Looks good!
 
  • Like
Likes 1 person
  • #3
Thank you!
 

Related to Thevenin equivalent of circuit and maximum power transfer

1. What is the Thevenin equivalent of a circuit?

The Thevenin equivalent of a circuit is a simplified circuit that represents the behavior of a more complex circuit. It consists of a single voltage source and a single resistor, and is used to analyze and solve complex circuits.

2. How is the Thevenin equivalent determined?

The Thevenin equivalent can be determined by first removing the load from the original circuit and calculating the open-circuit voltage (Voc) at the load terminals. Then, the equivalent resistance (Req) can be found by shorting out all voltage sources and calculating the total resistance seen from the load terminals. The Thevenin equivalent is then represented as Voc and Req in series.

3. What is maximum power transfer?

Maximum power transfer is the condition in a circuit where the load receives the maximum amount of power from the source. This occurs when the load resistance is equal to the Thevenin equivalent resistance of the circuit.

4. How can maximum power transfer be achieved?

Maximum power transfer can be achieved by adjusting the load resistance to match the Thevenin equivalent resistance of the circuit. This ensures that the load receives the maximum amount of power from the source.

5. What is the significance of Thevenin equivalent and maximum power transfer in circuit analysis?

The Thevenin equivalent and maximum power transfer are important concepts in circuit analysis as they allow for the simplification and optimization of complex circuits. They also help in determining the best load resistance for maximum power transfer, which is crucial in practical applications.

Similar threads

Engineering Finding the Thevenin Equivalent Circuit for a Network with a Load Resistor
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Why is the Thevenin resistance in this problem 3.2 kΩ?
    • Engineering and Comp Sci Homework Help
Replies
17
Views
2K
Engineering Find the Thevenin equivalent circuit
    • Engineering and Comp Sci Homework Help
2
Replies
42
Views
5K
Engineering Thevenin Theorem seems to not work in this 1 bit RAM RC circuit
    • Engineering and Comp Sci Homework Help
Replies
2
Views
997
Engineering Homework: Rx=? to get maximum power transfer at point M
    • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
Using the maximum power transfer theorem
    • Engineering and Comp Sci Homework Help
Replies
1
Views
2K
Engineering Maximum power transfer in a circuit
    • Engineering and Comp Sci Homework Help
Replies
1
Views
3K
Engineering How Do You Determine Thevenin Equivalent Circuits and Maximize Power Transfer?
    • Engineering and Comp Sci Homework Help
Replies
3
Views
1K
Calculating the Thevenin's Resistance of a Breadboarded Circuit
    • Engineering and Comp Sci Homework Help
Replies
9
Views
2K
Transmission Line, Max Real Power Transfer
    • Engineering and Comp Sci Homework Help
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top