How Do You Calculate Diagonal Resistance in a Circuit?

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SUMMARY

The discussion focuses on calculating diagonal resistance in electrical circuits, specifically using the formula for equivalent resistance in parallel and series configurations. Participants emphasize the importance of visualizing circuit layouts, particularly how to simplify complex arrangements by "stretching" wires to eliminate diagonal resistors. Key concepts include identifying short circuits and understanding current distribution in parallel resistors. The final approach involves calculating equivalent resistance by combining resistors in parallel and series sequentially.

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  • Understanding of Ohm's Law and resistance calculations
  • Familiarity with circuit diagrams and resistor configurations
  • Knowledge of series and parallel resistor combinations
  • Concept of short circuits and current paths in electrical circuits
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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.
 
Last edited by a moderator:
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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
 
short circuit
 
DAKONG said:
short circuit

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

- Warren
 
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
 
Last edited by a moderator:
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 ?
 
Consider this: if you put a piece of wire in parallel with a resistor, which path does the current take?

- Warren
 
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.
 
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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