# Equivalent electric circuit

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1. Oct 30, 2015

### Peter Velkov

Given an electric circuit, with resistors R1 and R2, find the equivalent resistance R.
Data: R1 = √2.R2

Points M and N have the same electric potential so they can be connected with a conductor and this way we get the second circuit.

2. Oct 30, 2015

### Staff: Mentor

There is more you can do to simplify the circuit.

3. Oct 30, 2015

### Peter Velkov

In terms of what? I know i can solve the parallel ones below, however that won't solve it. There should be a way to proof that M and N are also equal to O.

4. Oct 30, 2015

### Staff: Mentor

Sure, use symmetry again.

5. Oct 30, 2015

### Peter Velkov

It's symmetrical along MO, NO but that doesn't help us much.

6. Oct 30, 2015

### Staff: Mentor

Temporarily remove the two vertical R2's. What are the potentials at M,N,O?

7. Oct 30, 2015

### Peter Velkov

On the upper side we will have a resistor with √2R2, but on the down side R2/√2. So they will be different.

8. Oct 30, 2015

### Staff: Mentor

Really? What was your argument for M and N having the same potential in your first post?

9. Oct 30, 2015

### Peter Velkov

Equal amounts of charge will flow through the upper or downer R1, and since the resistance is equal the voltage will be too. However I don't understand why the points O and M or N will have the same potential as the resistance along the path is different.

10. Oct 30, 2015

### Staff: Mentor

The potentials at M,N, and O are due to the voltage dividers comprised of the resistances in their branches. Here's the situation:

All three branches have the same potential difference across them (whatever you imagine to be placed across terminals AB). All three branches have the same resistance ratios...