Hey all. The question I've been trying to solve is a bit of a doozie (for me, anyways), but I've broken it down to a point where I'm stuck. I'm given 3 resistors of unknown resistances. I have to construct a circuit, and then use that to figure out the resistance of each resistor. I'm given my source voltage, and I can measure the voltage across one component, and the current across one component.

The schematic I've come up with is essentially battery --- resistor 1 --- parallel branches with one resistor on each, and then looping back to my battery. I take the voltage and current across the first resistor and determine it's resistance. I can use that to calculate my total resistance, and then subtract R1 from my total resistance to get the sum of my parallel resistors. This is where I get stuck. I don't know how to use the values that I have found to solve for my other two resistances. I need to have the current of at least one of the branches (in my mind at least), so I really don't know where to go from here.

Any help would be greatly appreciated!!!

 

Source voltage IS the voltage across all the resistances in a circuit with all resistances in parallel, SO,,,,, we need something else. We can figure out the resistor for which the current is known, and thereby know what the other 2 are, if they are specified as all equal in value to each other, but not otherwise, if all 3 are parallel.

E=IR

An "Ohm meter" is actually a milliammeter driven by a known voltage.

 

I believe I would measure another resistor's drop and current......not R1. (with your circuit)

Can you see why?

 

What would the drop and current of R2 tell you?

 

What would the drop and current of R2 tell you?

That would show me the voltage of R3 as well, and from that I could determine V1, and R2. However, I then don't know how to find the current of R3 because I'm not quite sure how to find my source current from the numbers I would then have.


Edit: A quick schematic of my circuit

 

Hey all. The question I've been trying to solve is a bit of a doozie (for me, anyways), but I've broken it down to a point where I'm stuck. I'm given 3 resistors of unknown resistances. I have to construct a circuit, and then use that to figure out the resistance of each resistor. I'm given my source voltage, and I can measure the voltage across one component, and the current across one component.

The schematic I've come up with is essentially battery --- resistor 1 --- parallel branches with one resistor on each, and then looping back to my battery. I take the voltage and current across the first resistor and determine it's resistance. I can use that to calculate my total resistance, and then subtract R1 from my total resistance to get the sum of my parallel resistors. This is where I get stuck. I don't know how to use the values that I have found to solve for my other two resistances. I need to have the current of at least one of the branches (in my mind at least), so I really don't know where to go from here.

Any help would be greatly appreciated!!!

First, current doesn't go across things, it goes through things.

If I understand you correctly, you get to hook the voltage source (of known voltage) and the three unknown resistors up any way you want, but you get to measure the voltage across one resistor and you get to measure the current through one resistor (maybe the same one, maybe not). From this, you have to determine the values of all three resistors. Is that right?

Assuming it is, then how many fundamentally different ways are there to hook up the components? If there are only a few, then you might sketch each out and then ask, for each one, how many fundamentally different ways are there to take the two measurements. Again, if there aren't too many, then you might go through each of them and ask what information you can and cannot tease out of those measurements for that configuration.

 

I thought you said that you could only make one voltage measurement and one current measurement.

Forget about R1. What will the voltage drop across R2 tell you?

 

I'm not sure you can determine the value of three arbitrary resistors with only one voltage and one current measurement even if you know the source voltage also.

 

Sure you can.

Knowing the drop of R2 (EDIT: and current thru R2) tells you every parameter of circuit......because we know source V.

 

On the circuit you've diagrammed, given the battery's voltage, you'd want to know the voltage across R2, and the current through R2. Calc's are simple from there.

(As 549 implies and mentions, measurements across R1 aren't needed, they easily determined from R2 values)

 

Sure you can.

Knowing the drop of R2 (EDIT: and current thru R2) tells you every parameter of circuit......because we know source V.

On the circuit you've diagrammed, given the battery's voltage, you'd want to know the voltage across R2, and the current through R2. Calc's are simple from there.

(As 549 implies and mentions, measurements across R1 aren't needed, they easily determined from R2 values)

Really?

Let's say that the voltage supply is Vs = 10 V and that R1 = 5 kΩ, R2 = 10 kΩ, and R3 = 10 kΩ.

What would the voltage across and the current through R2 be?

Now let's say that the voltage supply is 10 V and that R1 = 8 kΩ, R2 = 10 kΩ, and R3 = 40 kΩ.

What would the voltage across and the current through R2 be?

Now let's say that the voltage supply is 10 V and that R1 = 910 Ω, R2 = 10 kΩ, and R3 = 1 kΩ.

What would the voltage across and the current through R2 be?

 

Knowing the drop of R2 (EDIT: and current thru R2) tells you every parameter of circuit......because we know source V.

Okay, so you can calculate the value of R2.
But I don't see how that tells us the value of R1 and R3, even if we know the source V.
You know the current of R1 and R3 in parallel and the voltage across them, but that's still not enough info.

 

I'm not sure you can determine the value of three arbitrary resistors with only one voltage and one current measurement even if you know the source voltage also.

If that's the case -- and since this is homework I'm not saying -- then the TS needs to prove that (or at least should need to prove that). I only see four fundamentally different ways of setting up the circuit, so all he has to do is to show that, for each of them, you are at best determining one of the resistances and setting up a relationship between the other two.

 

On the circuit you've diagrammed, given the battery's voltage, you'd want to know the voltage across R2, and the current through R2. Calc's are simple from there.

(As 549 implies and mentions, measurements across R1 aren't needed, they easily determined from R2 values)

Ok, I need a little more of a hint. To confirm - I know the source voltage. I can make one other voltage measurment - total and one current measurement. I then have to determine the values of all three unknown resistors.

If I know the voltage drop across R1, then I also now know the voltage drop across each of the parallel circuits that have R2 and R3

I then have a choice. I can then measure the current through R2 OR the current through R3. But I really need to know the source current to be able to establish the resistance of R1 or to understand how much current is left to flow through R3 (or R2 if I measured the current through R3 instead).

In my head, I just have too many variables to solve for. I guess I am stuck on Crutschow's comment.

 

You're right. I'm wrong. How about resistors in series and measure center drop and current anywhere.

 

Thank you all for your effort, my teacher just wrote to me and let me know that he screwed up the problem. I will be getting a new problem that's solvable to figure out.

 

You're right. I'm wrong. How about resistors in series and measure center drop and current anywhere.

Same thing. All you will have done is found what the sum of the other two resistances are with no way to determine how that resistance is split between them.

 

Thank you all for your effort, my teacher just wrote to me and let me know that he screwed up the problem. I will be getting a new problem that's solvable to figure out.

I would have left the problem but given anyone that attempted it full credit, anyone that determined that it had no answer some extra credit, and anyone that proved it even more.

There's a lot of thinking and learning that comes about by having to deal with problems that have no solution -- and you WILL run into such problems in real world engineering!

You might give some thought as to how you can prove it -- there's only four possibilities and two of them are degenerate (i.e., reduce to the same thing).

 

-Reading the voltages at a point between R1 and R2 let's you know the resistance values for R1 and the parallel combination of R2&R3.
-Knowing that you can calculate the current through the circuit.
-Now you measure the current through R2
- knowing the current through one element of the R2&R3 combo, as well as the current through both you figure out the current value of the second element of the R2&R3 combo.
- now we know the currents through, and the voltage across both elements of the R2&R3 combo, and calculate their individual resistance values.
- OK, now we know:
---voltages at all points of the circuit
---Current values through all elements
---Resistance values of all elements
---apparent power used and required

I myself don't know how much of that shouldn't be told to a given student in this forum, or perhaps the sequence some might suggest it be presented.

 

Does it let you know the resistance.......or the ratio of the resistance?