Wheatstone Bridge Explained

The Wheatstone Bridge is a special kind of electrical circuit used to measure a resistor’s resistance whose value we do not know.

The wheatstone bridge circuit diagram is as follows:

In the diagram, the unknown resistance R_x is to be measured; resistances R₁, R₂ and R₃ are known, where R₂ is adjustable. When the measured voltage V_G is 0, both legs have equal voltage ratios: R₂/R₁ = R_x/R₃ and

R_x= R₃R₂/R₁ (Wheatstone Bridge Formula)

Historical Context

Although popularized by Sir Charles Wheatstone, the inventor of this circuit was a scientist and mathematician by the name of Samuel Hunter Christie. 

He first described the circuit in 1883. As the circuit diagram, the bridge worked due to the diamond-shaped arrangement of the four resistors. Christie also described the experiment and the mathematics that is used to obtain the value of the unknown resistor.

Christie’s work remained relatively unknown, until Wheatstone, who was at that time a prominent member of the Royal Society of London, gave it a boost of publicity. In addition to bringing it into the public eye, Wheatstone improved the design. Wheatstone himself gave full credits of the invention to Christie. But in translations of Wheatstone’s lectures in Germany or France, this accreditation was missing. 

Wheatstone’s improvements helped to find not only resistance but also capacitances, inductances, frequencies, etc. by changing the elements contained in the legs. 

Theory and Derivation

This method to measure resistance works on the principle of null deflection. The current passing through the circuit can be visualised as follows:

At the balanced condition of the bridge, the current through the galvanometer arm is zero. In this case, 

I₁ = I₃ and 

I₂ = I₄

According to Kirchoff’s laws, the voltage drop across the arms of the loop is zero. 

I₁P = I₂R

i.e. I₁/I₂ = R/P

I₁Q = I₂S

i.e. I₁/I₂ = S/Q

Equating these two equations together, we get:

P/Q = R/S

Thus, if one of the resistance is unknown, we can use this formula to find the unknown resistance.

Experimentally, we use a setup similar to this: 

In this lab setup, we know that resistance is directly proportional to the length of the conductor, i.e. R = ρL/A.

Thus, the ratios of R3 and R4 in the given setup is just a ratio of their lengths. 

Limitations

Following are some limitation of the wheatstone bridge

1.  This device is susceptible. It is very easy to lose precision when using it for a long time. 
2.  It has a range of a few ohms to a few kilo-ohms.
3. If the resistances used in the device are not comparable, then the sensitivity of the device reduces.