Find all resistor values in the Wheatstone bridge

[Syle1]

Hi, I've got a small physics problem : build an thermometer using the Wheatstone bridge, only knowing the voltage and the middle resistor of the bridge.
I need help for the resistors values ; I've finished the rest, which is the relation between temperature and the resistors and the voltage.

I don't know how the find proper resistor values.

1. Homework Statement

Drew this : https://imgur.com/a/ESBuG

Homework Equations

Kirchhoff equations, Ohms law. Don't think more is needed?

The Attempt at a Solution

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Solved my initial problem (thermometer) by arbitrarily choosing R1 R2 R3 = 100 ohms, but it just seems so silly. I need to prove one way or another resistors values, or prove that I can arbitrarily choose them. (and which resistor range?)

Saw videos about solving the bridge knowing all the resistors, which I can do, but here we don't have them. So I have no idea ahah.Thanks a lot if you can help me through this, I'll owe you one !

Syle

 

[gneill]

Hi Syle1,

Welcome to Physics Forums!

You should think of any other design data or goals that might be pertinent. For example, presuming that Rx represents the temperature sensing device (thermistor?), do you know the range of resistance values it can take on over the desired temperature range? What would be a good potential difference to have across that part when its at the middle of its range?

How about total current draw for the circuit; is it battery operated? Larger resistor values will lower the total current draw...

 

[Syle1]

Hi Syle1,

Welcome to Physics Forums!

You should think of any other design data or goals that might be pertinent. For example, presuming that Rx represents the temperature sensing device (thermistor?), do you know the range of resistance values it can take on over the desired temperature range? What would be a good potential difference to have across that part when its at the middle of its range?

How about total current draw for the circuit; is it battery operated? Larger resistor values will lower the total current draw...

You understood perfectly my problem!

I think I started the wrong way ; instead of starting from the resistors values and then the relation between temperature and resistors, maybe I should start from the relation.

Lets get started, following your tracks.

1) Temperature range is fpr my greenhouse, so ideally the NTC thermistor Rx would be [ 0 ; 50 ] °C. (and that's a really big range)
Heres a simple resistance vs temperature table found on google, for NTC thermistors of course : http://www.weissinstruments.com/sg_userfiles/NTC_Chart.pdf

2) No clue how to find the potential difference showed on the voltmeter in the middle of the bridge when Rx is at 10k Ohms. (middle of my range, found on link)

3) As English isn't my main language, when you mean total current draw, do you mean V or I ? If its V, then yes it is battery operated. Standard 9V 1.2 Ah battery. If its I, no idea as we don't have equivalent resistance

Feel like going somewhere, thanks a lot !

 

[gneill]

You understood perfectly my problem!

I think I started the wrong way ; instead of starting from the resistors values and then the relation between temperature and resistors, maybe I should start from the relation.

Lets get started, following your tracks.

1) Temperature range is fpr my greenhouse, so ideally the NTC thermistor Rx would be [ 0 ; 50 ] °C. (and that's a really big range)
Heres a simple resistance vs temperature table found on google, for NTC thermistors of course : http://www.weissinstruments.com/sg_userfiles/NTC_Chart.pdf

Okay...

2) No clue how to find the potential difference showed on the voltmeter in the middle of the bridge when Rx is at 10k Ohms. (middle of my range, found on link)

3) As English isn't my main language, when you mean total current draw, do you mean V or I ? If its V, then yes it is battery operated. Standard 9V 1.2 Ah battery. If its I, no idea as we don't have equivalent resistance

I meant the current, $I$, that the 9 V battery needs to supply to power the circuit.

Looks like the middle of the desired temperature range (25 C) would have Rx at about 10 Ohms. That's a pretty small value for one leg of a bridge if your aim was to have the associated bridge node be at half the supply voltage at that value for Rx (you would need to choose R3 to be 10 Ohms also, and then that side of the bridge would only present 20 Ohms to the battery as a load, which would draw a lot of current, about 450 mA, and would mean a pretty short battery life for your 1.2 Ah battery).

Perhaps a better strategy would be to start with a reasonable total current draw based on how long you think the circuit should be able to operate on one 1.2 Ah battery. That will set the magnitude of the total resistance that each side of the bridge should have. Your lowest sensor resistance will be about 4 Ohms at 50 C, so R3 plus 4 Ohms should have the desired total resistance for a side (or, if you happen to know the operating temperature that the unit will be subjected to for the most time, use the Rx value associated with that value for your figuring). The resistors that make up the other side of the bridge can generally be chosen to be larger in sum so as to draw less current: their function, essentially, is to set a reference voltage against which the "bridge" measures the junction of the side with the sensor.

It'll then be up to the mysterious "10 k" bridge element to detect and present the resulting voltage range suitably.

Anyways, see what you can come up with regarding a "reasonable" total current for the circuit, then see what value R2 would have to have so that that side of the bridge (R2 + Rx) draws half or less than that value.