How Do You Calculate Equivalent Resistance in a Complex Circuit?

[oreosama]

Homework Statement

Hi, this was an extra credit problem on a test I had that I think I remember correctly

Given R find R equivilent of the circuit

Homework Equations

Series R1, R2 = R1 + R2
parallel R1, R2 = (1/R1 + 1/R2)^-1

The Attempt at a Solution

Never encountered a resistor in an awkward spot as the middle is, so I tried saying this:

since the upper path to Vb is an open wire it has Vo and the bottom path much match. To do this the voltage across these two must be 0 so we can just ignore them. From there you just have a parallel set left so

1/R + 1/2R = 3/2R -> 2R/3 = Req

 

[NascentOxygen]

Hi oreosama. From the left end of that 2R resistor, I see two parallel paths to get to point b.

 

[oreosama]

ive always understood parallel/series as a visual type thing. youre saying 1/R + 1/3R = 4/3R -> 3R/4 ? I Have no idea what this does to the circuit, as in where this combined resistor would be.. relative to the middle one still standing

 

[NascentOxygen]

I suggest that you redraw the circuit, drawing that middle resistor so this its symbol, too, is horizontal. Then connect the ends so electrically the circuit is identical with what you are given. Now, tidy it up so it looks like a neat circuit.

You might need to do this a couple of times, before you see how it simplifies.

 

[Nickie]

Hi there,

Thank you for sharing your extra credit problem with me. It seems like you have a good understanding of the equations for series and parallel resistors. Your approach to the problem is correct, and your solution of Req = 2R/3 is also correct. However, I would suggest showing your work step by step to make your solution clearer. Also, it might be helpful to label the resistors in the circuit so that it is easier to follow your solution.

In terms of the awkwardly placed resistor, it is important to remember that the voltage drop across a resistor in series is the same, so you can treat it as part of the overall resistance in the parallel set. I hope this helps and keep up the good work in your studies!