Equivalent resistance in a Wye formation

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SUMMARY

The discussion focuses on calculating the equivalent resistance in a Wye formation circuit while determining the Thévenin resistance by zeroing the sources. Participants clarify that after suppressing the current source, the only current path available is through the 20 Ω and 10 Ω resistors, leading to an equivalent resistance of 30 Ω. The conversation emphasizes the importance of visualizing a voltage or current source connected to the output terminals to understand the circuit's behavior and resistance. Techniques for analyzing more complex networks with controlled sources are also mentioned.

PREREQUISITES
  • Understanding of Thévenin's theorem and equivalent resistance
  • Familiarity with circuit analysis techniques, including source suppression
  • Knowledge of Wye (Y) and Delta (Δ) configurations
  • Proficiency in applying Ohm's law (R = V/I)
NEXT STEPS
  • Study the application of Thévenin's theorem in complex circuits
  • Learn about Wye-Delta transformations for circuit simplification
  • Explore techniques for analyzing circuits with controlled sources
  • Practice calculating equivalent resistance in various circuit configurations
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in circuit analysis and design who seeks to deepen their understanding of equivalent resistance and Thévenin's theorem.

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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After suppressing (opening) the current source, what closed paths are left for current to flow via the output terminals?
 
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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
 
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?
 
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?
 
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?
 
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)
 
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##.
 

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