Find the ratio of R1/R2

Thread Starter

PiNGUUUUUUU

Joined Aug 7, 2023
15
Hi, I need help solving the following problem, thank you in advance!

In the circuit shown in the figure, E = 5 V, R = 100 Ω, U1 = 3 V, U2 = 1 V. Find the ratio of R1/R2.

1692751564163.png
 

WBahn

Joined Mar 31, 2012
30,242
As this is pretty clearly an exercise of some kind, you need to show your best attempt to work the problem as far as you can. The more work you show, the better we can help you identify and overcome whatever is tripping you up.
 

Thread Starter

PiNGUUUUUUU

Joined Aug 7, 2023
15
Well its more like me trying to solve random circuits during summer break, but the problem is I don't even know where to start with this one, Ive tried writing both loop and node equations but there is always an extra unknown
 

WBahn

Joined Mar 31, 2012
30,242
Well its more like me trying to solve random circuits during summer break, but the problem is I don't even know where to start with this one, Ive tried writing both loop and node equations but there is always an extra unknown
Show your loop equations (or your node equations -- your pick).
 

WBahn

Joined Mar 31, 2012
30,242
If you show your loop (mesh) equations, I can almost bet I can help you see the additional equation that you need almost immediately.
 

WBahn

Joined Mar 31, 2012
30,242
I got to there and realized im missing something:/View attachment 301045
Your equations use I1 and I2 but you don't define what those are. Don't make us guess (and, more to the point, don't make yourself have to guess at some point or the grader guess when it's for credit).

Annotate your diagram with any voltages and currents you define as part of working the problem.
 

WBahn

Joined Mar 31, 2012
30,242
Assuming (and forcing people to assume is never a good thing) that I2 is the mesh current circulating clockwise in the right-hand mesh, can you look at the information in the problem and solve for I2 by inspection?
 

Thread Starter

PiNGUUUUUUU

Joined Aug 7, 2023
15
Assuming (and forcing people to assume is never a good thing) that I2 is the mesh current circulating clockwise in the right-hand mesh, can you look at the information in the problem and solve for I2 by inspection?
Yeah, you assumed correctly I1 is the mesh on the left and I2 is the mesh on the right both are circulating clockwise. Would I2 just be U2/R?
 

Thread Starter

PiNGUUUUUUU

Joined Aug 7, 2023
15
Hi, first of all i'd like to apologize for not answering for a week i've had a hectic few days. Would you mind clarifying some things for me please, because english is not my first language and i'm a little confused? Are my loop equations correct? And if they are am I just supposed to solve I2 or I1 and then i'm only left with R1 and R2 being unknowns so i just put that in the ratio?
 

WBahn

Joined Mar 31, 2012
30,242
Hi, first of all i'd like to apologize for not answering for a week i've had a hectic few days. Would you mind clarifying some things for me please, because english is not my first language and i'm a little confused? Are my loop equations correct? And if they are am I just supposed to solve I2 or I1 and then i'm only left with R1 and R2 being unknowns so i just put that in the ratio?
Yes, your loop equations are correct (I'm only looking at the top two equations).

You need to stop being sloppy with units in your work. R is not 100, it is 100 Ω, and E is not 5, it is 5 V.

You have two equations and four unknowns. So you need two additional equations.

The first you already have: I2 = U2/R = 1 V / 100 Ω = 10 mA

Can you see how to use the information that you normally would not be given (i.e., U1 and/or U2) to determine what I1 is?

Once you have that, you have two equations in two unknowns, namely R1 and R2. Solve for them and then find the ratio.

The question is arguably misleading because it implies that what matters is the ratio of R1 to R2, in the same sense that, on paper, a voltage divider only depends on the ratio of the two resistors and not their absolute values. But that is not the case here, there is a specific value that R1 has to be and a specific value that R2 has to be in order to get the values of U1 and U2 given in the problem.
 

WBahn

Joined Mar 31, 2012
30,242
So just to be 100% sure I1 is U1/R which is 30mA right?
Nope.

You are falling into the all-too-common trap of throwing the nearest voltage at Ohm's Law and hoping something sticks.

Remember, Ohm's Law relates a resistance of a resistor to the current through THAT resistor and the voltage across THAT resistor.

Is U1 the voltage across R?
 

Thread Starter

PiNGUUUUUUU

Joined Aug 7, 2023
15
Nope.

You are falling into the all-too-common trap of throwing the nearest voltage at Ohm's Law and hoping something sticks.

Remember, Ohm's Law relates a resistance of a resistor to the current through THAT resistor and the voltage across THAT resistor.

Is U1 the voltage across R?
So it would be E-U1 which is 5V-3V divided by R which is 100 Ω and that would make I1 20mA right?
 

WBahn

Joined Mar 31, 2012
30,242
So it would be E-U1 which is 5V-3V divided by R which is 100 Ω and that would make I1 20mA right?
Correct.

At this point, you can either solve your two loop equations using R1 and R2 as your unknowns, or you can continue an ad hoc analysis piecemeal, which is pretty simple for this problem.

You know the voltage to the left of the left-most R1, the current through that R1, and then you know the current through the right-most R1 and the voltage at the right of that R1. With just that you can solve for R1.
 

Thread Starter

PiNGUUUUUUU

Joined Aug 7, 2023
15
Correct.

At this point, you can either solve your two loop equations using R1 and R2 as your unknowns, or you can continue an ad hoc analysis piecemeal, which is pretty simple for this problem.

You know the voltage to the left of the left-most R1, the current through that R1, and then you know the current through the right-most R1 and the voltage at the right of that R1. With just that you can solve for R1.
Thank you very much, i couldn't have done it without your help!
 
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