How Do You Calculate Diagonal Resistance in a Circuit?

In summary, the homework statement says to find the equivalent resistance of a resistor consisting of three wires in parallel. However, the problem is much more complicated than that, and the student was not able to solve it.
  • #1
washablemarker
12
0

Homework Statement


http://img91.imageshack.us/img91/8346/resistorproblemim2.th.png
Find the equivalent resistance.

Homework Equations


equation for resistance. the variation used was 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ...

The Attempt at a Solution



i have no idea how to add the diagonal in.
 
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  • #2
Remember that you can stretch wires in any way you want to make the problem look simpler. Consider dragging the diagonal resistor, and the one to the right of it, to the right far enough that the diagonal resistor is no longer diagonal...

- Warren
 
  • #3
short circuit
 
  • #4
DAKONG said:
short circuit

And yes, that's what comes next. :wink:

- Warren
 
  • #5
chroot said:
Remember that you can stretch wires in any way you want to make the problem look simpler. Consider dragging the diagonal resistor, and the one to the right of it, to the right far enough that the diagonal resistor is no longer diagonal...

- Warren

oh, i see. but what do you mean by short circuit?

http://img82.imageshack.us/img82/3195/resistorproblembt3.th.png

edit: crap, i left something out. the problem was actually like the picture above. basically the same thing though.

so could i redraw the picture as to simplify it like this:

http://img526.imageshack.us/img526/7977/resistorproblemmodifiedji6.th.png
 
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  • #6
A short circuit is a condition whereby current passes through two nodes of a circuit (usually accidentally), without any resistance in between. Can you identify the short circuit in your circuit ?
 
  • #7
Consider this: if you put a piece of wire in parallel with a resistor, which path does the current take?

- Warren
 
  • #8
chroot said:
Consider this: if you put a piece of wire in parallel with a resistor, which path does the current take?

- Warren

the path of least resistance.
 
  • #9
arunbg said:
A short circuit is a condition whereby current passes through two nodes of a circuit (usually accidentally), without any resistance in between. Can you identify the short circuit in your circuit ?

so would that basically be a useless wire. in most situations anyway. but in the new diagram, there would be no short circuit.

(oops. sorry bout the double post. i meant to edit.)
 
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  • #10
Therefore... if you put a piece of wire in parallel with ANYTHING, the parallel combination acts just like a piece of wire by itself.

- Warren
 
  • #11
washablemarker said:
the path of least resistance.

Just to clear things up, if you have resistances in parallel, it doesn't essentially mean that the current passes only through the one with the least resistance, current gets divided in each of the branches, but the greatest current flows through the one with least resistance. In the case of short circuit in one of the branches (0 resistance) only, does all current pass through that particular 'piece of wire'.

In your edited question, you don't require this concept, and the way you have redrawn the circuit appears correct.
 
  • #12
http://img151.imageshack.us/img151/7763/isthiscorrectgr1.th.png

correct me if I'm wrong.

the resistors in red are in parallel, so you can add them together with the equation of parallel resistance.

then the resultant would be in series with the blue resistor, so you could simply add them together.

now the resultant of that would be in parallel with the green resistor, so you can calculate their total with the equation again.

then the resultant of that would be in series with the rest, so you could add them all together to find the total or equivalent resistance.

arunbg said:
Just to clear things up, if you have resistances in parallel, it doesn't essentially mean that the current passes only through the one with the least resistance, current gets divided in each of the branches, but the greatest current flows through the one with least resistance. In the case of short circuit in one of the branches (0 resistance) only, does all current pass through that particular 'piece of wire'.

yeah. i knew that current is divided up. i was had meant, the greater amount flows through the smaller resistor. nice catch, but as for you question. i don't know. would it.

arunbg said:
In your edited question, you don't require this concept, and the way you have redrawn the circuit appears correct.

alright, that's good. thank you.
 
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  • #13
You got it.

- Warren
 
  • #14
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FAQ: How Do You Calculate Diagonal Resistance in a Circuit?

What is diagonal resistance in a circuit?

Diagonal resistance in a circuit refers to the resistance that is present in the diagonal path of a circuit. This can occur when a circuit has multiple components connected in a diagonal manner, creating a longer path for the flow of current.

Why does diagonal resistance occur?

Diagonal resistance occurs due to the physical layout of the circuit. When components are connected in a diagonal manner, it creates a longer path for the current to flow through, resulting in an increase in resistance.

How does diagonal resistance affect the performance of a circuit?

Diagonal resistance can affect the performance of a circuit by increasing the overall resistance and reducing the efficiency of the circuit. This can lead to a decrease in the amount of current that reaches the desired components, resulting in a decrease in performance.

How can diagonal resistance be reduced?

Diagonal resistance can be reduced by using shorter and more direct paths for the flow of current in a circuit. This can be achieved by rearranging the components or using alternative circuit designs that minimize diagonal connections.

What are the consequences of high diagonal resistance in a circuit?

High diagonal resistance in a circuit can cause overheating, voltage drops, and overall reduced performance. It can also lead to the failure of certain components or the entire circuit. Therefore, it is important to consider and minimize diagonal resistance when designing a circuit.

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