Total resistance through cubic circuit

In summary, the problem asks to find the equivalent resistance between two diagonally opposite corners of a cube with 12 resistors, each lying along an edge and connected at the corners. To solve this problem, Kirchhoff's laws can be applied by considering the cube as a flat shape or by counting the connections at each node.
  • #1
Fizzicist
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Homework Statement



Suppose a resistor R lies along each edge of a cube (12 resistors in all) with connections at the corners. Find the equivalent resistance between two diagonally opposite corners of the cube


Homework Equations



[tex]\Sigma[/tex]I = 0 at a node (a junction)

[tex]\Sigma[/tex]V = 0 through a loop

V=IR

The Attempt at a Solution




Not quite sure how to do this one algebraically. Would I just add up all the V/Is? how?
 
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  • #2
Not quite sure where to start...can anyone help me?
 
  • #3
How about opening the cube out so it's flat and looking at it that way.
 
  • #4
Interesting...is that necessary though, or could I just apply kirchhoffs laws to it as it is?
 
  • #5
I count from anyone node:
3 paths to 3 nodes which then connect by:
6 paths to 3 nodes which then connect by:
3 paths to 1 node.

connecting the 3 nodes together with wires should change nothing.
 
  • #6
are you saying just ignore those 6 connections?
 
  • #7
I think the post I was responding to was deleted.
 

FAQ: Total resistance through cubic circuit

1. What is total resistance through a cubic circuit?

Total resistance through a cubic circuit is the overall resistance that an electric current encounters when flowing through a circuit that consists of three resistors arranged in a cubic shape.

2. How is total resistance calculated in a cubic circuit?

In a cubic circuit, the total resistance is calculated by using the formula Rt = R1 + R2 + R3 + 2(R1R2 + R2R3 + R1R3). This takes into account both the individual resistances as well as the interactions between the resistors.

3. What factors affect the total resistance in a cubic circuit?

The total resistance in a cubic circuit is affected by the individual resistances of the three resistors, as well as their arrangement in the circuit. Additionally, the material and thickness of the wires connecting the resistors can also impact the total resistance.

4. Can the total resistance in a cubic circuit ever be zero?

No, the total resistance in a cubic circuit can never be zero. This is because the resistors in the circuit will always have some amount of resistance, and the formula for total resistance takes into account all three resistors.

5. How can the total resistance in a cubic circuit be reduced?

The total resistance in a cubic circuit can be reduced by using resistors with lower individual resistances, arranging the resistors in a parallel configuration instead of a series, and using thicker wires with lower resistance to connect the resistors.

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