Finding Thevenin Equivalent Circuit for a Complex Network

In summary, the student replaced all the resistors with red lines, but does not know how to combine resistances when there are short circuits. This implies the student does not know how to solve equations.
  • #1
Shawkify
5
0

Homework Statement


74df2061fc.png


Homework Equations


Thevenin Equivalents
V = IR

The Attempt at a Solution


402c55e6e5.png

To try to find R_th, I replaced all the voltages with short circuits but I do not what to do next.

Then I believe V_th would just be the same as the voltage of the rightmost resistor.
 
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  • #2
Shawkify said:
...I do not know how to combine resistances when there are short circuits.
That implies you do not know how to combine resistances at all. I mean, if you take two series resistance, there is a short circuit (aka "a wire") between the two and it's even worse with parallel resistors since they have short circuits (aka "wires") between pairs of ends.
 
  • #3
All points joined together by a short-circuit become a single node. So redraw the resistor circuit simplified by condensing nodes along each short-circuit wire into a single node.
 
  • #4
NascentOxygen said:
All points joined together by a short-circuit become a single node. So redraw the resistor circuit simplified by condensing nodes along each short-circuit wire into a single node.
5faadd80df.png

This is how I ended up reducing the circuit, was this correct?
 
  • #5
We are interested only in the resistance seen by the 2 external terminals. Other bits and pieces can be ignored.
 
  • #6
Would the resistance just then be 3R?
 
  • #7
Shawkify said:
Would the resistance just then be 3R?
No. Where is your simplified circuit showing the external terminals?

A consequence of a resistor having its ends shorted together is that no current will flow in that resistor (there being zero PD across it) so you can omit it from the circuit.
 
  • #8
See if this helps.

Starting diagram:
I've replaced resistors with red lines.
The short circuit jumpers are shown in black.

upload_2017-1-27_21-37-21.png

The blue arrows show the direction the short circuit jumpers will collapse to the center.

Let's just take the upper left section and see what happens when we collapse its short circuit jumper.

upload_2017-1-27_21-39-45.png


Now I have two resistors connected between the outside and the inside of the diagram. The straight red line is the original resistor and the curved red one is the one which moves due to the short circuit jumper.

This leads to an equivalent R/2 between those points.

You need to pursue this with the rest of the circuit and see what you get.

Sorry I didn't have the energy to draw resistors but I hope you get the point.
 

What is a Thevenin Equivalent Circuit?

A Thevenin Equivalent Circuit is a simplified representation of a complex network of resistors, voltage sources, and current sources. It consists of a single voltage source in series with a single equivalent resistance, and can be used to analyze the behavior of a circuit without having to consider the details of the internal components.

How is a Thevenin Equivalent Circuit calculated?

To calculate the Thevenin Equivalent Circuit, the circuit is first disconnected from the load and all voltage sources are shorted. The equivalent resistance is then determined by finding the resistance between the two points where the load was connected. The equivalent voltage is found by measuring the voltage across those two points.

What is the purpose of a Thevenin Equivalent Circuit?

The Thevenin Equivalent Circuit is used to simplify complex networks and make circuit analysis easier. It is also useful in predicting the behavior of a circuit under different load conditions and in designing efficient circuitry.

What are the limitations of a Thevenin Equivalent Circuit?

The Thevenin Equivalent Circuit assumes that the internal components of the network are linear and can be represented by a single voltage source and resistance. It also only applies to DC circuits and does not take into account the effects of capacitance or inductance.

Can a Thevenin Equivalent Circuit be used for non-linear circuits?

No, a Thevenin Equivalent Circuit is only applicable to linear circuits. Non-linear circuits, such as those with diodes or transistors, cannot be simplified in the same way and require more complex analysis methods.

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