# To reduce the resistance

In the circuit I need to find out equivalence Resistance.

I have applied the Kirchhoff theorem and but these look too broad and might take too much time to solve. Is there any easy way to solve it?>

EDIT: So if the vertical resistor doesn't apply any affect to the voltage then the equivalent resistance will be, $$1/(R_e)=1/2R+1/2R+1/2R$$ That means $$R_e=2/3R$$ . Is it right?? but the question is why the vertical resistor is not applying voltage changes to the circuit??? Are they acting as only voltage divisor, nothing else?

• Yeah, your intuition is correct, there are real shortcuts. You should be able to solve it by inspection if you take symmetry into account. See one of the suggested solutions to this problem: electronics.stackexchange.com/questions/105207/… Apr 9, 2014 at 6:49
• They have answered a particular question. Can you please apply-the symmetry in this circuit then I will get clearly. I'm saying this because they have not explained much :( Apr 9, 2014 at 7:00
• As a gendankenexperiment, leave out the vertical R's. Assuming the battery is 0V, What is the voltage on each of the (remaining) R/R junctions? Apr 9, 2014 at 7:02
• If the battery is zero volts then how can we get the voltage across these resistors? Will they 0 volts too right? Apr 9, 2014 at 7:04
• What Wouter is implying I'll say a different way - what current is flowing thru the vertical resistors - ask your self what voltage would appear on each node of the vertical resistors. This is a strongish hint. Apr 9, 2014 at 7:06

Here is a great way to look at a problem where all resistances are equivalent:

1. Intuition: Lets (temporarily) remove the vertical resistors and attempt to analyze the problem. After removing the vertical resistors, lets look at what elements exist at the nodes of the voltage source:

• Connected between both nodes are 3 branches in parallel
• Inside of each branch are 2 resistors in series.

Since all three branches are identical, lets look at only a single branch first. Lets call the node in between the two resitors "MiddleNode". We apply voltage division and we find that that voltage at MiddleNode is 0.5*Vsource (because both resistors are identical).

Note that the MiddleNode voltage is identical on each of the three branches.

So if we look at the potential difference (voltage drop) between two MiddleNodes, we find that the voltage drop will be 0V. If you have a 0V potential difference between two nodes (two MiddleNodes in our case), no current will flow through an element placed there. Hence, the vertical resistors play no role.

2. Solution: You have 3 branches in parallel with 2R resistance per branch.

2R//2R//2R = (2/3)R