# Simple Voltage Divider Algebra problem

#### ECE101

Joined Nov 25, 2011
29
1: Vout = Vin.R2 / R2 + R1

2: (R2 + R1). Vout = Vin. R2

3: (-R2. Vin + R2) + R1. V out = 0

4: R2(-Vn +1) + R1.Vout = 0

5: R2 = (R1.Vout) / (Vin + 1)

How does one go from line 2, to line 3?

I end up with:

2: (R2 + R1). Vout = Vin. R2

3: (-R2. Vin) + R2. Vout + R1. Vout = 0

#### hgmjr

Joined Jan 28, 2005
9,029
1: Vout = Vin.R2 / R2 + R1

2: (R2 + R1). Vout = Vin. R2

3: (-R2. Vin + R2) + R1. V out = 0

4: R2(-Vn +1) + R1.Vout = 0

5: R2 = (R1.Vout) / (Vin + 1)
Loks like there is and error between line 2 and line 3 above.

How does one go from line 2, to line 3?

I end up with:

2: (R2 + R1). Vout = Vin. R2

3: (-R2. Vin) + R2. Vout + R1. Vout = 0

hgmjr

• ECE101

#### ECE101

Joined Nov 25, 2011
29
2: (R2 + R1). Vout = Vin. R2

3: (-R2. Vin) + R2. Vout + R1. Vout = 0

So in terms of R2:

3: (-R2. Vin) + R2. Vout + R1. Vout = 0

4: R2(Vout - Vin) + R1. Vout = 0

5: R2 = -R1. Vout / (Vout - Vin)

Is this correct?

If so how is the following derived here? #### hgmjr

Joined Jan 28, 2005
9,029
All you should need to do is divide the numerator and the denominator by the value Vout. Remember that whatever you do the denominator, you must do to the numerator to perserve the equality.

hgmjr

• ECE101

#### ECE101

Joined Nov 25, 2011
29

#### ECE101

Joined Nov 25, 2011
29
Thanks again for the reply hgmjr

I'm still having a problem getting the wiki answer though!

1: Vout = Vin.R2 / R2 + R1

2: (R2 + R1). Vout = Vin. R2

3: (R2 + R1). Vout/Vin = R2

4: R2(Vout/Vin - 1) + R1(Vout/Vin) = 0

5: R2 = -R1(Vout/Vin)/(Vout/Vin - 1) ?

#### hgmjr

Joined Jan 28, 2005
9,029
I can see why.

The transition from 3 to 4 is a case of taking too big a bite. It should have been split up into two seperate steps.

hgmjr

hgmjr

• ECE101

#### ECE101

Joined Nov 25, 2011
29
Got it! Cheers:

Vout/Vin = R2/R1+R2
(R1 + R2) (Vout/Vin) = R2
R1 (Vout/Vin) + R2 (Vout/Vin) - R2 = 0
R1 (Vout/Vin) = R2 - R2 (Vout/Vin)
R1 = R2(Vin/Vout) - R2
R1 = R2((Vin/Vout) - 1)
R2 = R1/((Vin/Vout) - 1)

#### WBahn

Joined Mar 31, 2012
25,918
A couple of times now you have written:

Vout/Vin = R2/R1+R2
(R1 + R2) (Vout/Vin) = R2
The second line doesn't follow from your first line, except when whoever is doing the work opts to replace the first line with what you meant to write and not what you actually wrote.

What you wrote is:

Vout/Vin = (R2/R1)+R2

Since division has precedence over addition. It's an easy mistake to make, which makes it all the more critical that you develop the habit of not making it very often.

#### WBahn

Joined Mar 31, 2012
25,918
1: Vout = Vin.R2 / R2 + R1
2: (R2 + R1). Vout = Vin. R2
3: (-R2. Vin + R2) + R1. V out = 0
4: R2(-Vn +1) + R1.Vout = 0
5: R2 = (R1.Vout) / (Vin + 1)

How does one go from line 2, to line 3?
Look at line 3 carefully. Do the units work out? No. The first term has units of volt-ohms while the second just has units of ohms. You can't add the two. You KNOW the equation is incorrect. There is no point even looking at what comes after it, because it is guaranteed to be WRONG (unless another error just happens to fix the first).

Having said that, let's look at what comes next. In equation three, you have (-Vn + 1). Most people, since they don't track units, won't be bothered by this at all because, being sloppy, they are used to seeing crap like this all the time. But, again, the units don't work. Vn (should be Vin, BTW) has units of volts and 1 is dimensionless and, if you were in the habit of tracking units, just seeing this would SCREAM out to you ERROR! ERROR! ERROR!