Multimeter Exercise

Tuesday February 28th, 2012

With the aid of a Wheatstone bride and a multimeter, anyone can create a simple resistance thermometer. The basic schematic for a Wheatstone bridge can be viewed to the right. To create a resistance thermometer using this device, chose 4 nearly identical resistors and put them on the four legs of the bridge. If they are sufficiently balanced, the voltage (V) should be nearly zero.


Once you have verified that this works, you can remove one leg of the bridge and extend it using wire or alligator clips. In the picture below, one leg has been removed and white alligator clips have been used to extend the length of the bridge. This is done so that the 4th resistor can be brought into contact with different substances and can be used as the probe in our thermometer.

A multimeter, set to voltage, is connected across the bridge, which in this photo is attached to the top green clip and the bottom right white clip.

As you can see from this photo, the multimeter reads 22.4 millivolts, which is a reasonable difference based on the tolerances of the resistors used. When the 4th resistor is dipped in an ice bath for 3 minutes, the voltage changes by approximately 14 millivolts. When the resistor is removed from the bath, it eventually returns to it's original reading of 22.4 millivolts. This reading is repeatable, and if the ice bath is 0 degrees Celsius, and the ambient temperature is approximately 20 degrees Celsius then we can use the equation for the temperature dependence of resistance to create a thermometer.

A wheatstone bridge is a non-linear circuit, meaning that as the resistance in the 4th element continues to change, the voltage across the bridge is not strictly linear. It obeys the following formula.

Vout = I*Ro*(Ro^2 *α*(T − T₀))/(2*Ro+Ro*(2+α*(T − T₀))

Where I is current, Ro is the original resistance of the each resistor, α is the temperature coefficient of resistance for the element in question, and T and T₀ are the final and initial temperatures.


Though non-linear, it deviates from a line by no more than one percent as long as the change in temperature is small, say less than 30 degrees Celsius.

So we can model this function as:

T=k(V-Vo) where k is a constant which describes our system. In this case, k would be 1.43 degrees Celcius/millvolt.


R(T) = R₀[1 + α(T − T₀)]