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I need to find the total resistance that is seen from terminals a and b for the three circuits below.

enter image description here

I found that all of the circuits have the same total resistance Rt=R (not sure if the answer is correct.) Also, there is no current flowing through c-d and the voltage across c-d is the same for every circuit (LTspice simulation.)

Is it safe to say it's just the same balanced Wheatstone bridge circuit written in three different ways or are there any big differences between the circuits?

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2 Answers 2

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I need to find the total resistance that is seen from terminals a and b

Just think about the implications of what I wrote on the picture below: -

enter image description here

So, for all three scenarios it makes no difference how you connect points c and d; the impedance looking into a and b will be the same.

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Maybe your b) network is clearer this way :

enter image description here

By symmetry you can see that the potential at c and d are equals. Thus, no current flows from c to d.

This is the same as saying that adding a resistance between them does not change the overall resistance.

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  • \$\begingroup\$ So for b) we can just flip the terminals b and d? Wouldn't that somehow be bad? Can we do the same for a) and c) too? \$\endgroup\$
    – kauselis3000
    Commented Apr 23, 2023 at 12:46
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    \$\begingroup\$ @kauselis3000 Become adept at re-arranging these circuits as InfinteLooper has done. It is a skill that helps greatly in analyzing circuits. \$\endgroup\$
    – glen_geek
    Commented Apr 23, 2023 at 13:01
  • \$\begingroup\$ @kauselis3000, What ? for a)and c) just add the corresponding resistance or wire between c and d \$\endgroup\$
    – InfiniteLooper
    Commented Apr 23, 2023 at 13:11
  • \$\begingroup\$ You don't flip nothing. It's just an other representation of the same thing \$\endgroup\$
    – InfiniteLooper
    Commented Apr 23, 2023 at 13:13

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