Effective Resistance in a Circuit (with many paths)

In summary, the question is asking for the effective resistance between nodes E and F, which can be found by taking into account the extra paths. For parallel paths, the resistance is equivalent to the sum of the resistances of the individual paths.
  • #1
cavalieregi
41
0

Homework Statement


Hi I am working on a study task. This is the schematic of the circuit. (all resistors are 1 k ohms.)
ic6qvL4.jpg

I need to calculate the following values of resistance that will be seen between the pairs of nodes, indicated by the subscripts.

REF , RCD and RAB

(That is, REF refers to the total resistive effect between node E and node F. This is the resistance that would be 'felt' or 'seen' by a current injected at node E and extracted at node F. Multiple paths means multiple options, and a lowering of the effective resistance.

2. The attempt at a solution
I understand how to calculate effective resistance for series or parallel although I am not sure how I would approach this as I am confused by the alternative paths and hence how to lower effective resistance between the nodes.
 
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  • #2
Not sure what you mean by "Alternative paths"? Parallel paths ?

Just have a go and show your working so we can see where/if you have gone wrong.
 
  • #3
CWatters said:
Not sure what you mean by "Alternative paths"? Parallel paths ?

Just have a go and show your working so we can see where/if you have gone wrong.

Okay for example if current was injected into node E the resistance between E and F going up would be 1k ohms + 1k ohms + 1k ohms = 3k ohms but that current could also flow through the right path and resistance between E and F would be = 1k ohm. This would be the other path.

The question states 'REF refers to the total resistive effect between node E and node F. This is the resistance that would be 'felt' or 'seen' by a current injected at node E and extracted at node F. Multiple paths means multiple options, and a lowering of the effective resistance.'

I am not sure how you would get this effective resistance considering the many paths the current could take.
 
  • #4
cavalieigit: 4897347 said:
I am not sure how you would get this effective resistance considering the many paths the current could take.
Many paths?? How many exactly, for E-F?

These are parallel paths here. You know how to caculate the resultant resistance for resistors in parallel?
 
  • #5
RT = 1/(1/R1+1/R2+...+1/RN) right. I am just confused by the question as it says if you inject current at node E here will it travel via the right or up to get to node F. We need to find effective resistance between the nodes. The questions says you must take into account these extra paths to the node F.
 
  • #6
Current will make its way taking all available paths. The easiest path will carry a heavier current, the path of highest resistance will carry the least current. These currents are always in accord with Ohm's Law.

If the paths are parallel, you can treat them as resistors in parallel and calculate a single equivalent resistance of the multiple paths.
 
  • #7
Okay for example if current was injected into node E the resistance between E and F going up would be 1k ohms + 1k ohms + 1k ohms = 3k ohms but that current could also flow through the right path and resistance between E and F would be = 1k ohm. This would be the other path.

There are actually three paths between E and F...

a) R6+R5+R2
b) R3
c) R4 (assuming the one on the right is R4)

These are all in parallel with each other so the equivalent resistance is

REF = (R6+R5+R2) // R3 // R4

where // means "in parallel".
 
  • #8
CWatters said:
There are actually three paths between E and F...

a) R6+R5+R2
b) R3
c) R4 (assuming the one on the right is R4)

These are all in parallel with each other so the equivalent resistance is

REF = (R6+R5+R2) // R3 // R4

where // means "in parallel".

Cheers this answers all my questions.
 

FAQ: Effective Resistance in a Circuit (with many paths)

What is effective resistance in a circuit?

The effective resistance in a circuit is the overall resistance experienced by current flowing through the circuit. It takes into account all of the individual resistances in the circuit and their arrangement.

How is effective resistance calculated in a circuit?

The effective resistance can be calculated using different methods depending on the circuit's complexity. For simple circuits with only series or parallel components, it can be calculated using Ohm's Law and the rules for series and parallel resistors. For more complex circuits, the use of Kirchhoff's laws and mathematical equations is necessary.

Why is it important to understand effective resistance in a circuit?

Understanding effective resistance is crucial for designing and analyzing circuits. It helps in determining the amount of current flowing through the circuit and the voltage drop across different components. It also helps in predicting the behavior of the circuit under different conditions and in troubleshooting any issues that may arise.

What factors affect the effective resistance in a circuit?

The effective resistance in a circuit is affected by the arrangement of components, the type of components used, and the material of the components. It also depends on the temperature, length, and cross-sectional area of the conductors, as well as the frequency of the current flowing through the circuit.

How can the effective resistance in a circuit be reduced?

The effective resistance in a circuit can be reduced by adding resistors in parallel, which decreases the overall resistance, or by using conductors with larger cross-sectional areas to reduce the resistance of the wires. Additionally, using materials with lower resistivity and keeping the circuit at a lower temperature can also help in reducing the effective resistance.

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