How Do You Calculate Diagonal Resistance in a Circuit?

[washablemarker]

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.

 

[chroot]

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

 

[DAKONG]

short circuit

 

[chroot]

short circuit

And yes, that's what comes next.

- Warren

 

[washablemarker]

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

 

[arunbg]

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 ?

 

[chroot]

Consider this: if you put a piece of wire in parallel with a resistor, which path does the current take?

- Warren

 

[washablemarker]

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.

 

[washablemarker]

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.)

 

[chroot]

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

 

[arunbg]

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.

 

[washablemarker]

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.

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.

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.

 

[chroot]

You got it.

- Warren

 

[washablemarker]

You got it.

- Warren

yes. somewhat too late though. this had been a test question and i hadn't realized they are just wires.

in case anybody needs it.

http://img220.imageshack.us/img220/4162/explanationwhyia9.th.png