Method of Symmetry for Equivalent Resistances

In summary, the method of symmetry in circuit analysis simplifies the evaluation of equivalent resistances by connecting nodes with the same potential and using the rules for parallel and series components. This method assumes that symmetrically located points have the same potential, which can be applied to resistors of equal value. For asymmetrical circuits, different methods may need to be used. Textbooks such as "Understanding Physics" by DC Pandey can provide further explanations and examples.
  • #1
Swapnil Das
15
6
Member advised to use the homework template for posts in the homework sections of PF.
I have been studying the method of symmetry from some days, which essentially reduce the effort needed for the evaluation of equivalent resistances. My textbook states:

Points having symmetrically located about initial and final points have the same potentials.So, the resistances between these points can be ignored.
Understanding Physics, DC Pandey

Okay, fine. Problems get solved,but I have some questions regarding this.

  • Why does the method of symmetry work?
  • Does the method only apply for resistors of equal value/magnitude?
  • If yes, then how do we deal with asymmetrical circuit of resistors, say, in a cube?
  • And most essentially, how do we define symmetry?

Please help me. If you can, please recommend some JEE Physics Textbooks too.

Thanks!

Swapnil Das
 
Physics news on Phys.org
  • #2
Nodes that are at the same potential can be connected together without affecting the circuit. This then allows you to simplify the circuit using the rules for parallel and series components.
 
  • #3
CWatters said:
Nodes that are at the same potential can be connected together without affecting the circuit. This then allows you to simplify the circuit using the rules for parallel and series components.
But how does the method assume that they are at the same potential?
 
  • #4
Swapnil Das said:
But how does the method assume that they are at the same potential?

Do you understand how a Potential Divider works?

What happens if you scale all the resistors in a Potential Divider circuit?
 
  • Like
Likes Swapnil Das
  • #5
CWatters said:
Do you understand how a Potential Divider works?

What happens if you scale all the resistors in a Potential Divider circuit?
Are they at the same potential? Is it the same principle out there?
 
  • #6
Yes.
 
  • #7
CWatters said:
Yes.
Thanks, wonderful explanation!
 

1. How does the Method of Symmetry for Equivalent Resistances work?

The Method of Symmetry for Equivalent Resistances is a technique used to simplify complex circuits and determine the equivalent resistance. It involves identifying symmetrical parts of the circuit and combining them to reduce the overall complexity. This method relies on the principle that symmetrical components have equal resistance, and thus can be combined into a single equivalent resistance.

2. Is the Method of Symmetry for Equivalent Resistances always accurate?

While the Method of Symmetry for Equivalent Resistances is a useful tool for simplifying circuits, it may not always provide an accurate result. This method assumes that the circuit is perfectly symmetrical, which may not always be the case. Additionally, it only considers the resistance values and does not take into account other factors such as capacitance or inductance.

3. Can the Method of Symmetry for Equivalent Resistances be applied to all types of circuits?

The Method of Symmetry for Equivalent Resistances can be applied to circuits with both series and parallel combinations of resistors. However, it may not be applicable to circuits with non-linear components such as diodes or transistors.

4. How do you know when to use the Method of Symmetry for Equivalent Resistances?

The Method of Symmetry for Equivalent Resistances is most useful for circuits with multiple identical symmetrical components. It can be used to simplify the circuit and make it easier to analyze. It is also helpful when trying to find the equivalent resistance of a circuit with many resistors in series or parallel.

5. Are there any limitations to using the Method of Symmetry for Equivalent Resistances?

One limitation of the Method of Symmetry for Equivalent Resistances is that it can only be used to simplify circuits with symmetrical components. It also does not take into account the effects of non-ideal components such as resistors with varying resistance values. Additionally, this method may not be suitable for circuits with a large number of resistors, as it can become time-consuming and complex to identify symmetrical parts.

Similar threads

Find the equivalent resistance of this circuit
    • Introductory Physics Homework Help
Replies
28
Views
1K
Finding Equivalent Resistance Using Symmetry and Kirchhoff's Laws
    • Introductory Physics Homework Help
Replies
3
Views
825
How can I calculate the equivalent resistance of this circuit?
    • Introductory Physics Homework Help
Replies
9
Views
1K
Why do the headlights on the car become dim when the car is starting?
    • Introductory Physics Homework Help
Replies
4
Views
265
Removing connections between equipotential points in solving circuits?
    • Introductory Physics Homework Help
Replies
10
Views
1K
Equivalent resistance of pentagon of resistors
    • Introductory Physics Homework Help
Replies
13
Views
5K
Find the equivalent resistance (Req) of the simple circuit.
    • Introductory Physics Homework Help
Replies
4
Views
3K
Find the equivalent model of an infinite ladder circuit
    • Introductory Physics Homework Help
Replies
3
Views
3K
Equivalent resistance of 2015 points
    • Introductory Physics Homework Help
Replies
31
Views
2K
What is the relationship between resistors in a circuit?
    • Introductory Physics Homework Help
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top