I was asked to find a value of R2 to make the diode current = .25 mA on a recent quiz. I breezed through most of the quiz and thought it seemed extremely simple but completely hit a wall with this question and tried everything I knew including node and mesh analysis which usually works for me but everything I did resulted in me having too many unknowns since the value of R3 isn't given. I ran out of time after trying for an hour and a half on this and it is still bugging me a day later. Can someone explain this to me, because it seems very difficult in comparison to the rest of the quiz so I must be doing something very wrong. Thanks in advance.

 

Were you told what the forward voltage drop across the diode should be?

 

Give the answer in terms of R3. Even better, give it in terms of R3 and Vd (i.e., don't use a numerical value for the forward diode drop since you can't give a numerical value for R3 anyway).

 

I was asked to find a value of R2 to make the diode current = .25 mA on a recent quiz. I breezed through most of the quiz and thought it seemed extremely simple but completely hit a wall with this question and tried everything I knew including node and mesh analysis which usually works for me but everything I did resulted in me having too many unknowns since the value of R3 isn't given. I ran out of time after trying for an hour and a half on this and it is still bugging me a day later. Can someone explain this to me, because it seems very difficult in comparison to the rest of the quiz so I must be doing something very wrong. Thanks in advance.
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Hi,

I have to agree that we dont know some things here like the value of resistor R3, but we also do not know anything at all about what diode model is being used. You can only get that from knowing what the typical diode model was that you used in previous problems in the course or on the test.

Without this information all we can do is come up with a symbolic solution, or else provide some sort of general description such as, "The larger R2 is allowed to be the closer R3 becomes to the resistance value of 18k".

But judging by your screen name, maybe you could ask some "body" else

 

To clarify we assume a .7 V drop across the diode, I know that the voltage across R2, will be .7 V more than R3, but I am still confused how I would find the value of R2 needed without knowing R3, I always end up with one too many unknowns, even if I replace the diode and R3 with a .25 mA current source leaving the node.

 

To clarify we assume a .7 V drop across the diode, I know that the voltage across R2, will be .7 V more than R3, but I am still confused how I would find the value of R2 needed without knowing R3, I always end up with one too many unknowns, even if I replace the diode and R3 with a .25 mA current source leaving the node.

What if the diode wasn't there? Can you solve it? That is, in terms of R3. If you don't see that, then assume R2 = R3 and work from there.

 

That problem is somewhat ambiguous.
Doesn't the problem ask to find the value of R3 also?
As shown, there is more than one value of R2 and R3 that will solve the problem.

 

As shown, there is more than one value of R2 and R3 that will solve the problem.

R2 could be open and there is a answer for R3.

 

What if the diode wasn't there? Can you solve it? That is, in terms of R3. If you don't see that, then assume R2 = R3 and work from there.

I am not denying this is the solution but can you clarify why I can make this assumption? If I assume they are equal, that would mean the current draw and voltage would be equal, and I don’t understand how I could make this assumption

 

R2 could be open and there is a answer for R3.

Wouldn’t this value for R3 need to change if the current remains constant at .25 mA and I put another resistor in parallel which would draw some of the current going through that branch?

 

Wouldn’t this value for R3 need to change if the current remains constant at .25 mA and I put another resistor in parallel which would draw some of the current going through that branch?

Would it? A basic tenet describes how current acts in this case. In other words, how does current behave differently when two circuits (resistors?) are wired in series versus the same two circuits are wired in parallel? What happens if you have a lamp plugged in your house, and you plug in another lamp? Does the first lamp dim?

 

Would it? A basic tenet describes how current acts in this case. In other words, how does current behave differently when two circuits (resistors?) are wired in series versus the same two circuits are wired in parallel? What happens if you have a lamp plugged in your house, and you plug in another lamp? Does the first lamp dim?

The current would be divided among the branches in parallel but the voltage would stay the same so the two branches in the problem would have the same voltage but the currents would be different and when I write node equations I change to a .25 mA current source to simplify it and I have two unknowns still which are the voltage at the node and R2, and if I try to write mesh equations I run into issues with the current in the branch for the same reason. I have always thought this understanding to be correct, what am I missing?

 

Hello again,

You are not missing anything. As we have been saying, there is no way to solve this for one particular value of R2.

The simple answer is that the value of R2 depends on both the voltage across the diode AND the values of R3. If you assume the diode voltage is 0.7v or even 0.0v then we still dont know the value of R3, and the value of R2 changes drastically with the value of R3. This means that the only solution is symbolic in that it must include at least the value of R3 in order to actually calculate a numerical value for R2. Some problems are like this, and indeed every problem can be stated as a symbolic solution but in this case we dont have any choice.

For a couple examples with the diode voltage being zero, if R3=18k then R2 is infinite.
If R3=9k then R2=R1=30k
If R3=4.5k then R2=10k
If R3=2k then R2=3.75k
So you can quickly see that as the value of R3 changes, the value of R2 changes.
If you make the diode voltage 0.7v then you get different values but R2 still varies with R3. So we can state this as:
R2=f(vd, R3)
which just says that R2 is a function of both the diode voltage and the value of R3.

If you change the diode into a constant current source of 0.25ma then the value of R3 does not matter in the determination of the current though that branch, but it is not enough to be able to determine the node voltage at the junction of R1 and R2 and the diode. This means we still can not calculate a single value for R2.

This is certainly not the only problem like this. There are many problems that do not have a single solution because something else is not known yet.
Perhaps they have left something out, such as to calculate the maximum value of R2, or maybe the minimum value or something else like that. In fact maybe the answer is "there is no single solution for R2".

 

To clarify we assume a .7 V drop across the diode, I know that the voltage across R2, will be .7 V more than R3, but I am still confused how I would find the value of R2 needed without knowing R3, I always end up with one too many unknowns, even if I replace the diode and R3 with a .25 mA current source leaving the node.

Again, give the answer for R2 in terms of the value for R3.

Consider the classic voltage divider with R1 "on top" of R2 such that the output voltage is

Vout = Vin * R2/(R1 + R2)

If asked to find R1 such that Vout = 3 V when Vin = 12 V, you can answer this, without knowing the actual value of R2, in terms of R2:

R1 = [(Vin/Vout) - 1] * R2

R1 = 3*R2

 

Damn! That's tricky!
Right. Off we go. . . .

Let V2 be the voltage across R2, and Vs be the supply voltage.
V2 = 250uA.R3+Vd
The total current is (Vs-V2)/R1. The current through R2 is 250uA less than that
V2/R2 = (Vs-V2)/R1 -250uA
Expand the brackets
V2/R2 = Vs/R1 - V2/R1 - 250uA

V2/R2 = Vs/R1 - V2/R1 - 250uA.R1/R1

Round up the R1's
V2/R2 = (Vs-V2-250uA.R1)/R1
Divide by V2
1/R2 = (Vs-V2-250uA.R1)/(R1.V2)
Turn it upside down
R2 = (R1.V2)/ (Vs-V2-250uA.R1)
Expand out V2
R2 = (R1.(250uA.R3+Vd))/ (Vs-(250uA.R3+Vd)-250uA.R1)

R2 = (R1.(250uA.R3+Vd))/ (Vs-Vd-250uA.(R3+R1)

Try it out with R3 = 10k, and Vd = 0.7
V2 = 3.2V
R2 calculates to 96k/1.3 =73.85k

Current through R2 =3.2V/73.85k = 43.33uA
Current through R1 = (12-3.2)/30k = 293.33uA
293.33uA - 43.33uA = 250uA, which is the current through R3.

Quad Erat Demonstrandum

. . . but I still think that there must be an easier way.

 

Hello again,

You are not missing anything. As we have been saying, there is no way to solve this for one particular value of R2.

The simple answer is that the value of R2 depends on both the voltage across the diode AND the values of R3. If you assume the diode voltage is 0.7v or even 0.0v then we still dont know the value of R3, and the value of R2 changes drastically with the value of R3. This means that the only solution is symbolic in that it must include at least the value of R3 in order to actually calculate a numerical value for R2. Some problems are like this, and indeed every problem can be stated as a symbolic solution but in this case we dont have any choice.

For a couple examples with the diode voltage being zero, if R3=18k then R2 is infinite.
If R3=9k then R2=R1=30k
If R3=4.5k then R2=10k
If R3=2k then R2=3.75k
So you can quickly see that as the value of R3 changes, the value of R2 changes.
If you make the diode voltage 0.7v then you get different values but R2 still varies with R3. So we can state this as:
R2=f(vd, R3)
which just says that R2 is a function of both the diode voltage and the value of R3.

If you change the diode into a constant current source of 0.25ma then the value of R3 does not matter in the determination of the current though that branch, but it is not enough to be able to determine the node voltage at the junction of R1 and R2 and the diode. This means we still can not calculate a single value for R2.

This is certainly not the only problem like this. There are many problems that do not have a single solution because something else is not known yet.
Perhaps they have left something out, such as to calculate the maximum value of R2, or maybe the minimum value or something else like that. In fact maybe the answer is "there is no single solution for R2".

I have a feeling the value of R3 was accidentally cropped out, the rest of the quiz was incredibly simple and there was no indication whatsoever they wanted an expression or a number for R3. I was able to come to a value of R2 expressed in terms of R3 but was about to pull my hair out trying to figure this problem out. There was another problem unrelated that also incredibly vague and I had no idea how to solve it even with access to the textbook, but saw a similar problem in the chapter that had a little more information

 

Just solve the problem symbolically!

It's four lines to set up the physics (the EE stuff) and about a half-dozen or so lines of eighth-grade algebra to solve for R3.

 

Thank you for all the help, I

Just solve the problem symbolically!

It's four lines to set up the physics (the EE stuff) and about a half-dozen or so lines of eighth-grade algebra to solve for R3.

The question is to solve for R2 though, and the only way I can do that is by assuming a value of R3, and there was nothing mentioned about it, and it seemed like the teacher wanted an exact value

 

You're right, it would be completely trivial with the value of R3 known, but R3 can't be eliminated from the equations.

 

Think of it in terms of "what does R2 have to do"? Why is it even in the circuit?