R Network- finding total resistance.

[GDGirl]

Homework Statement

Assuming R = R' = 1.97 Ω in the network shown above, determine the net resistance

a) between the points a and c
b) between points a and b.
HELP: Use symmetry.
HELP: Imagine applying a voltage between a and c and think about what current will flow in each resistor.

https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/Knox/phys130a/spring/homework/09/02/P26_36.jpg

Homework Equations

Series: R_total=R₁+R₂
Parallel: R_total=(R₁^-1+R₂^-1)^-1

The Attempt at a Solution

Well, I redrew the series in my notebook as parallel and series, but in both attempts at a re-draw, I ended up with a weird branch that wasn't really either series or parallel, because of how it connected. I tried solving it anyway (and have come up with 1.313 for the resistance between a and c) but nothing's been right. I'm just not sure what to do with the weird branch. :/

 

[LowlyPion]

Observe that with all the resistors equal to each other that you can drop out the R' resistors that cross between the || branches. At each leg of your || you have a voltage divider with no net voltage across the R'. This should make your calculation a bit easier.

For instance between AC:

1/R + 1/2R + 1/2R = 1/Rac

 

[GDGirl]

Oh wow, that makes things a lot simpler. I wasn't aware that I could drop out that resistor. Thank you!