Finding Equivalent Resistance in a Circuit

Click For Summary
SUMMARY

The discussion focuses on finding the equivalent resistance in a circuit using node voltage analysis and test sources. The participant initially struggles with the concept but ultimately resolves the problem by applying Kirchhoff's Current Law (KCL) after placing a test voltage source across the terminals. The correct approach involves recognizing that the voltage across the input resistor is determined solely by the voltage source, regardless of other voltages in the circuit. The final answer is confirmed as correct, demonstrating the effectiveness of using a test source in circuit analysis.

PREREQUISITES
  • Understanding of node voltage analysis
  • Familiarity with Kirchhoff's Current Law (KCL)
  • Basic knowledge of equivalent resistance concepts
  • Experience with circuit analysis techniques, including test sources
NEXT STEPS
  • Study advanced node voltage analysis techniques
  • Learn about controlled sources in circuit analysis
  • Explore the application of Thevenin's and Norton's theorems
  • Investigate common pitfalls in circuit analysis and how to avoid them
USEFUL FOR

Electrical engineering students, circuit designers, and anyone looking to enhance their understanding of circuit analysis and equivalent resistance calculations.

mnvaughn
Messages
9
Reaction score
0

Homework Statement


The problem wants me to find the equivalent resistance at the terminals. Here is the circuit plus some of my work. The Answer according to the teacher is C.
http://i.imgur.com/JaW7f.jpg


Homework Equations





The Attempt at a Solution


As seen from my work, I added a test source. By doing this I'm trying to solve for I norton so i can divide the test source by I norton for the resistance. I start doing node voltage analysis at the node closest to the test voltage. From the calculations I find the voltage of the node farthest of the voltage source to be 2 volts. I then use node voltage at that node to solve for i0. I found i0 to be 3/4A however after that I'm completely lost.
 
Physics news on Phys.org
Surely if you put a voltage supply v across ab then the current io will be v/1Ω.
 
But isn't there a voltage at the bottom too? so it i0=v1/2i0?
 
mnvaughn said:
But isn't there a voltage at the bottom too? so it i0=v1/2i0?

If you place a voltage source across a-b, that voltage and no other will appear across the 1 Ohm resistor at the input terminals.
 
if it was that simple then why isn't the answer just 1? I'm really confused on why you disregard the voltage at the bottom. Underneath the 1ohm resister is not ground but another voltage which is 2i0.
 
mnvaughn said:
if it was that simple then why isn't the answer just 1? I'm really confused on why you disregard the voltage at the bottom. Underneath the 1ohm resister is not ground but another voltage which is 2i0.

io is the current through that "input" resistor, and is so defined by the circuit diagram. Call it R. You place a voltage source V across that resistor R and the resulting current through that resistor is V/R. It doesn't matter what the potential at b is because node a is V volts greater than that due to that voltage source. If V is an ideal voltage source, NOTHING can alter that.

Note that io is not the total current being "pushed" into the circuit by V. There are still calculations to do to find that!
 
what would be your suggestion to go from here then? Do i not use a test source? because i really don't know any other way to solve it then.
 
mnvaughn said:
what would be your suggestion to go from here then? Do i not use a test source? because i really don't know any other way to solve it then.

Yes, use a test source (I thought that was what the recent exchange concerned!).

If you place a test voltage source Vin across the input a-b, then you immediately know the current io. This gives you the controlled source values. From there look at writing KCL node equations. Start with the node that the current source flows into.
 
WOW. I'm SOOO STUPID. I did that exactly and i got it. Thanks that problem even stumped my professor in class. Thank you soooo much
 
  • #10
mnvaughn said:
WOW. I'm SOOO STUPID. I did that exactly and i got it. Thanks that problem even stumped my professor in class. Thank you soooo much

We aim to please :biggrin:
 

Similar threads

Engineering How do I find Vth with the node voltage method?
  • · Replies 10 ·
Replies
10
Views
4K
Engineering Why is the voltage source high potential into node 1 at -12 V in this op amp problem?
  • · Replies 15 ·
Replies
15
Views
2K
Engineering Norton/Thevenin Equivalent circuits with a dependent voltage source
  • · Replies 9 ·
Replies
9
Views
6K
Equivalent resistance with a capacitor
  • · Replies 11 ·
Replies
11
Views
8K
Find the Norton equivalent resistance
  • · Replies 2 ·
Replies
2
Views
2K
Engineering Create a circuit in simulation to prove my work (2 batteries and 1 lamp bulb)
  • · Replies 5 ·
Replies
5
Views
2K
Engineering Create the Thevevenin equivalent circuit
  • · Replies 12 ·
Replies
12
Views
2K
How to find the equivalent resistance of this electric circuit?
  • · Replies 5 ·
Replies
5
Views
4K
I finding the Thevenin equivalent resistance
  • · Replies 6 ·
Replies
6
Views
2K
Engineering Attempt at Thevenin Equivalent Circuit
  • · Replies 8 ·
Replies
8
Views
3K