Use Wheatstone bridge to measure unknown resistance

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A new look at the old bridge

Can we now, in the 21st century, look at this famous 19th century device from a different perspective? Let's try... we won't lose anything from this... we will only gain…

There were no precise sources then (neither voltage nor current)... nor precise voltmeters. So they had to find a way to compensate for the errors (mainly because of the varying supply voltage).

For this purpose, they used the principle of negative feedback but implemented manually. So, the so-called "balanced bridge" and the man moving the rheostat's wiper or switching the resistors inside the box is a "negative feedback system". Its main purpose is to convert an unknown resistance Rx into another known (readable, measurable) resistance Rvar. It make it by keeping equal the ratios of two voltage dividers.

From this point of view, the balanced bridge can be considered as a "resistance-to-resistance converter". Depending on the ratio determined by the rest two resistors, there are three possible cases:

• Rvar = Rx - "resistance follower"
• Rvar > Rx - "resistance multiplier"
• Rvar < Rx - "resistance divider"

The "output resistance" Rvar could be converted to length (by the so-called "rheochord") or could be presented as a sum of discrete resistors (in a box).

How we measure resistance today

Today, practically we do not use a bridge to measure resistance because we have precise current sources and digital voltmeters (both implemented by the negative feedback principle).

So we simply pass a reference current Iref through the unknown resistance Rx and measure the voltage Vout across the resistance; then we calculate Rx = Vout/Iref, according to Ohm's law. This is how modern ohmmeters are made.