- #1
zetologos
- 1
- 0
Homework Statement
I don't know where to start. Can anyone recommend a book the instructor didn't assign one.
Equivalent resistance between points a and b
- Thread starter zetologos
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SUMMARY
The discussion focuses on calculating equivalent resistance between points A and B in a circuit with multiple resistors. Key methods include analyzing current flow using Ohm's Law (V=IR) and considering the configuration of resistors in series and parallel. Participants emphasize the importance of symmetry in simplifying the circuit analysis, particularly when identifying nodes with the same voltage. The approach involves setting up equations based on the arrangement of resistors and may lead to solving quadratic equations for complex configurations.
PREREQUISITES- Understanding of Ohm's Law (V=IR)
- Knowledge of series and parallel resistor combinations
- Familiarity with circuit analysis techniques
- Basic algebra for solving equations
- Study the principles of series and parallel circuits in detail
- Learn how to apply Kirchhoff's laws in circuit analysis
- Explore methods for simplifying complex resistor networks
- Practice solving quadratic equations in the context of electrical circuits
Students studying electrical engineering, physics enthusiasts, and anyone looking to improve their skills in circuit analysis and equivalent resistance calculations.
I don't know where to start. Can anyone recommend a book the instructor didn't assign one.
- #2
ideasrule
Homework Helper
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I don't think a book is necessary, as long as you know how to find the equivalent resistances for parallel and series circuits. For the first question, imagine a current I entering at A and leaving through B. How much current will flow through each of the resistors? You can use this to figure out the voltage drop between the two points.
For the second question, suppose I take off the 3 resistors at the very right. What would the equivalent resistance be between the top-right point and the bottom-right point? You can use this to set up an equation to solve for the equivalent resistance.
For the second question, suppose I take off the 3 resistors at the very right. What would the equivalent resistance be between the top-right point and the bottom-right point? You can use this to set up an equation to solve for the equivalent resistance.
- #3
MATLABdude
Science Advisor
- 1,663
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Welcome to PhysicsForums!
These are more math / problem solving-type questions, rather than straightforward circuit analysis.
Here's a hint for a: consider what happens when you inject a test current 'I_o' into point A, and figure out how the current flows. Then figure out the voltage at each point (V=IR)
For b, consider that you're adding three series resistors in parallel with a single one. And then you're adding another three series resistors in parallel with the one resistor that you just added previously. Consider: you're far down the line, does adding another three resistors change the equivalent resistance by very much? You should end up solving a quadratic equation using this approach.
Good luck!
EDIT: Obviously, adding three resistors at that point changes the resistance at that point. It shouldn't change the resistance very much at the beginning of your resistor chain.
These are more math / problem solving-type questions, rather than straightforward circuit analysis.
Here's a hint for a: consider what happens when you inject a test current 'I_o' into point A, and figure out how the current flows. Then figure out the voltage at each point (V=IR)
For b, consider that you're adding three series resistors in parallel with a single one. And then you're adding another three series resistors in parallel with the one resistor that you just added previously. Consider: you're far down the line, does adding another three resistors change the equivalent resistance by very much? You should end up solving a quadratic equation using this approach.
Good luck!
EDIT: Obviously, adding three resistors at that point changes the resistance at that point. It shouldn't change the resistance very much at the beginning of your resistor chain.
- #4
pgardn
- 656
- 2
The second diagram looks too easy if Points A and B on the circuit are the far right top and bottom "corners" on the circuit. There is only one resistor between points A and B? What am I missing?
- #5
gneill
Mentor
- 20,989
- 2,934
pgardn said:
All the other paths from A to B that pass through all the other resistors
- #6
vk6kro
Science Advisor
- 4,079
- 41
The first one is done by joining together (with wires) points on the cube that must have the same voltage on them, by symmetry.
If they have the same voltage, no current will flow in the new wires, but they make the problem a lot easier. You get a few sets of parallel resistors in series.
If they have the same voltage, no current will flow in the new wires, but they make the problem a lot easier. You get a few sets of parallel resistors in series.