Potential divider textbook example. Confused.

[illy]

Hi,

I am just going through a textbook on electronics and have come across an explanation that uses potential dividers to work out potential values for resistors. I was wondering if anyone is able to explain how the author got the bit after "which can be written as": R1=(4.9/10.1)*R2

How did he rearrange it to get this? Any help would be appreciated. Thank you! (I have added the pictures from the textbook.)

 

[Baluncore]

The same current flows through R1 as R2. The voltage across R1+R2 = 15V
The voltage Vout across R2 = 4.9V
So voltage across R1 = 15V – 4.9V = 10.1V
The ratios R1 / R2 = 10.1V / 4.9V

Therefore R1 = ( 10.1 / 4.9 ) * R2
So maybe the second equation cannot be rewritten as R1 = ( 4.9 / 10.1 ) * R2

 

[jim hardy]

How did he rearrange it to get this?

That's algebra not electronics

solve for R1 ?

There are several paths to get there
i would

1. divide both sides by 4.9
2. multiply both sides by (R1 + R2)
3. subtract from both sides R2

and when you do that you'll find author's mistake