Resistance Measurements

Your customer wants you to do a high-current test to monitor the performance of welded connections in a conductor (see sketch). For this a nominal current of 500 A is fed into a system with an uncertainty of 1A. The nominal resistance of the weld is 1 mOhm +/- 5%. 

a) The resistance can be monitored by two measurement systems. System A has an absolute 25 mV measurement tolerance defined for the 5V nominal measurement range. System B has a 1% measurement tolerance of its nominal value. The nominal value of system B is 2 V. Which of the voltage measurement systems are you going to use to have a minimum measurement uncertainty for the measurement? Explain why!

b)  What is the relative measurement error for a single welded connection with the connection being at a nominal level using your chosen measurement system?

As the measurement of a single welded connection is very tiring and time-consuming, several welded connection are put in series according to the sketch below. 

For 10 welds (resembled by resistances) the equivalent circuit looks like the figure below. 

If you want to measure at the voltage across one measurement point, you need to subtract two voltages. As the voltages are in the range of "volt" only and we need to identify changes in the range of % an amplification of 10 is going to be realized.

For the measurement, you have ideal resistors and ideal operational amplifiers available (no tolerances).

c) Become creative: Design a circuit which can be used to measure the voltage across one resistor/weld (substract two voltages) and amplify this differential-voltage! Explain with a couple of sentences how it works!

d) Your stock shows resistors of 1kOhm, 2kOhm, 5k Ohm and 10kOhm (all ideal, without tolerance), you have an unlimited number of resistors available. You want to measure the voltage V₄ between measurement points MP3 and MP4. Take your circuit from c) and define where to use which resistor to achieve an amplification of a factor of 10 for the differential voltage!

e) You use a 10 bit ADC with an input range of 16V for the amplified signal according to your circuit as dimensioned in d). In how many digits change will the tolerance of +/- 5% result in? Explain your calculation.