# Help with multiple unknown resistances in a series/parallel circuit

#### tbfunk

Joined Dec 9, 2010
30
Hi, to be honest this isnt actually homework for any course however since I am interested in learning I guess its personal homework. That being said I really want to try to understand what I am not seeing here and be able to solve it.

So in the enclosed simple circuit I have a DC voltage source powering resistors in series and in parallel.
My known values are as such:
R3 Has a voltage drop of 12v and is using 0.25A
V1 is a 30v regulated source

My question is can I solve for R1 and R2 or do I not have enough information?

I have read through once (so far) the Volume I - Direct Current on this site and am trying to apply the concepts but I seem to be stuck.
I think R1 has a voltage drop of 18v and I also think R3 is 48 ohms however thats about as far as I have gotten.

#### Jony130

Joined Feb 17, 2009
5,162
In parallel circuit the voltage is the same. This is because all resistor are connected between the same two points. So in your circuit R2 and R3 are connected in parallel. So to be able to find a R2 resistor value you need to know the current. And you are right about the voltage drop across R1.
And from the I Kirchhoff's law we know that IR1 = IR2+IR3

#### WBahn

Joined Mar 31, 2012
25,738
For each unknown resistance you need an additional piece of (independent) information that you otherwise would not need to know had you been given all the resistances. You only have two such additional pieces. Thus it is unlikely that you will be able to determine all three resistances, though you can determine constraints and required relationships, such as R1 can't be any bigger than this or that the ratio of R2 to R1 has to be that.

One way to determine whether you have sufficient information is to see if you can arbitrarily pick two a values for one (or more) of the unknowns and still solve for the rest in such a way that you satisfy the original problem statement. That, by itself, is not a good sign. But it's possible that you just happen to pick the one value that it had to have. So pick a different value and see if you can still solve the problem. If you can, then you definitely did not have enough information to completely solve the problem.

You are correct about the value of R3 -- it has to be 48 Ω. You are also correct about the voltage drop across R1 (going from left to right) -- it has to be 18 V.

But now assume that R2 is really, really big (so that it is effectively an open circuit). Can you find a value of R1 that will satisfy the problem statement?

Then assume that R2 is the same size as R3. Can you find a value of R1 that will satisfy the problem statement?

If you can do both, then the problem as stated is indeterminate.