Determining the equivalent resistance of an irreducible network of resistors

In summary, the question is asking for a faster way to find the equivalent resistance of a network without having to solve a large system of equations. The options given are to either use Kirchoff's laws and solve a system of equations or use a Δ-Y transformation on one of the resistor loops to simplify the network. However, exploiting symmetry in the given resistor values may also be a quicker solution.
  • #1
richyw
180
0

Homework Statement



Alright so I am having trouble finding the equivalent resistance of something like this

8236711208_093498af9d_z.jpg


Without "hooking it up" to a current source and solving a large system of equations to find the voltage drop across the network and therefore the resistance.

Is there a faster way to do this (say in an exam situation)?

Homework Equations



-kirchoffs laws
-parallel/series equivalent resistances
V=IR

The Attempt at a Solution



As I described gets me the answer. Want to know if it is the quickest way!
 
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  • #2
Unless there's a symmetry to exploit with the given values of the resistors (so that the potentials at either end of resistor R3 must be equal), there are two choices:

1. Add a supply and write three loop or nodal equations and solve

2. Use a Δ-Y transformation on one of the resistor loops and continue reducing the network
 

FAQ: Determining the equivalent resistance of an irreducible network of resistors

1. How do you determine the equivalent resistance of an irreducible network of resistors?

The equivalent resistance of an irreducible network of resistors can be determined using Ohm's Law, which states that resistance is equal to voltage divided by current. This can be applied to each individual resistor in the network and then the resistances can be added together to find the total equivalent resistance.

2. What is an irreducible network of resistors?

An irreducible network of resistors is a circuit in which the resistors are arranged in a way that they cannot be simplified or reduced to a simpler form. This means that the resistors cannot be combined in series or parallel to simplify the circuit.

3. Why is it important to determine the equivalent resistance of a network of resistors?

Determining the equivalent resistance of a network of resistors is important because it allows us to calculate the total resistance in a circuit, which is necessary for understanding the flow of current and the amount of voltage drop in the circuit. This information is crucial in designing and analyzing electronic circuits.

4. Can the equivalent resistance of an irreducible network of resistors be negative?

No, the equivalent resistance of an irreducible network of resistors cannot be negative. Resistance is a physical quantity that can only have positive values, therefore, the equivalent resistance of a network of resistors can never be negative.

5. Are there any other methods for determining the equivalent resistance of an irreducible network of resistors?

Yes, there are several other methods for determining the equivalent resistance of an irreducible network of resistors, such as using Kirchhoff's laws, Thevenin's theorem, and Norton's theorem. These methods can be used as alternatives to Ohm's Law, depending on the complexity of the circuit and the desired outcome.

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