Equivalent resistance in a Wye formation

In summary, the conversation discusses finding the Thevenin resistance for various circuits by zeroing the sources and analyzing the closed paths for current flow. It is mentioned that the equivalent resistance can be found by imagining a source connected across the output terminals and applying Ohm's law. This technique is useful for more complex networks with controlled sources.
  • #1
Frankenstein19
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Homework Statement


Find the Thévenin resistance for each of the circuits shown by zeroing the sources.
upload_2017-12-7_12-8-1.png

Homework Equations

The Attempt at a Solution


I replaced the current source with an open circuit and I'm left with a wye formation but I don't know how to calculate the equivalent resistance
 

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  • #2
After suppressing (opening) the current source, what closed paths are left for current to flow via the output terminals?
 
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  • #3
gneill said:
After suppressing (opening) the current source, what closed paths are left for current to flow via the output terminals?
None? It'll just look like a T
 
  • #4
Frankenstein19 said:
None? It'll just look like a T
Yes, but suppose you were to apply a voltage (or current) source across the two output terminals. What path or paths could current follow? Remember, a "circuit" implies a closed path (loop).

Edit: Remember that in finding the Thevenin equivalent, you want to find the circuit's equivalent resistance "looking into" the output terminals. What load resistance would a test source "see" if connected there?
 
  • #5
gneill said:
Yes, but suppose you were to apply a voltage (or current) source across the two output terminals. What path or paths could current follow? Remember, a "circuit" implies a closed path (loop).
Sorry if I'm nor using correct terminology but through the 20 an 10 ohm resistor?
 
  • #6
Frankenstein19 said:
Sorry if I'm nor using correct terminology but through the 20 an 10 ohm resistor?
Correct! The 5 Ω resistor, being disconnected at one end, is unable to pass a current through it. So the only path available is the one you've identified.

So then, what's the equivalent resistance?
 
  • #7
gneill said:
Correct! The 5 Ω resistor, being disconnected at one end, is unable to pass a current through it. So the only path available is the one you've identified.

So then, what's the equivalent resistance?
30! Haha bless your soul for spoon feeding this to me. But I'm still a little confused as to why I'd suppose there was a source connected to the output terminals. I wasn't doing that with previous exercises. (I'll try it though to confirm)
 
  • #8
Frankenstein19 said:
30! Haha bless your soul for spoon feeding this to me. But I'm still a little confused as to why I'd suppose there was a source connected to the output terminals. I wasn't doing that with previous exercises. (I'll try it though to confirm)
The idea is that the network presents a certain resistance at the output terminals. A resistance can pass current through it. Hence, if you imagine that there is a source connected across it, then only the paths that can pass current can be involved in the net resistance.

When you come across more complex networks with controlled sources (rather than fixed voltage and current sources) that you cannot suppress, one of the techniques that you'll have to employ is to apply a fixed source to the terminals and then analyze the resulting current and voltage that results through and across the terminals in order to use Ohm's law to determine the "load" resistance: ##R = V/I##.
 

1. What is Equivalent Resistance in a Wye formation?

Equivalent resistance is the total resistance experienced by an electrical circuit in a Wye formation, which is a type of circuit configuration where three resistors are connected in a triangular shape.

2. How is Equivalent Resistance calculated in a Wye formation?

To calculate Equivalent Resistance in a Wye formation, you can use the formula: 1/Req = 1/R1 + 1/R2 + 1/R3, where Req is the Equivalent Resistance and R1, R2, and R3 are the individual resistances of the three resistors in the circuit.

3. What is the significance of Equivalent Resistance in a Wye formation?

Equivalent Resistance is important in a Wye formation because it helps simplify complex circuits and allows us to easily calculate the total resistance in the circuit. It is also used to determine the amount of current that will flow through the circuit.

4. How does Equivalent Resistance impact the overall performance of a Wye formation circuit?

The value of Equivalent Resistance in a Wye formation determines the amount of current that will flow through the circuit. A higher Equivalent Resistance means that less current will flow through the circuit, while a lower Equivalent Resistance means that more current will flow through the circuit.

5. Can Equivalent Resistance be calculated for circuits with more than three resistors in a Wye formation?

Yes, Equivalent Resistance can be calculated for circuits with any number of resistors in a Wye formation. The formula for calculating it remains the same, where the number of resistors is represented by the variable "n" in the equation: 1/Req = 1/R1 + 1/R2 +...+ 1/Rn.

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