What is Wheatstone Bridge?

What is Wheatstone Bridge?The  bridge was first developed by Samul Hunter Charlie in 1833and it is popularized Chalie Wheatstone in 1843 .It is used for measuring accurately the value of an unknown resistance.

Although today the digital multimeter is used to measure the resistance in a simple way but the Wheatstone bridge are still used to measure the low resistance in the range of milli-ohms ranges.

Now adays wheatstone bridge are use in various electronic circuits such as with the modern operation amplifier we used it to interface various sensors and transducers with these amplifier circuit.

The Wheatstone bridge is a simple series-parallel circuit of resistance which is connected between the voltage terminal and the ground ,which produced the zero voltage difference between the two parallel branch when it is in balance condition. It has two input terminal and two output terminals consisting four resistors which is configured in the shape of diamond as shown in the figure.

Construction

It consist of four resistors (two fixed resistances P and O which are known, one variable resistance R which is also known and one unknown resistance X whose value is to be found) . Across one pair of opposite junctions (A and C) battery is connected and across the other opposite pair of junctions (B and D), a galvanometer is connected.

WORKING

The value of P and Q are properly fixed. When the key is switched on. the current divide unequally between the two branches and  galvanometer shows current. The value of resistance R is varied until the galvanometer shows zero current. Under such conditions the bridge is said to be balance

The point at which the bridge is balanced is called null point. Let l₁ and l₂ be the current  through P and R respectively when the bridges is balance . Since there is no current  through  the Galvanometer the current in Q and X are aIso l₁ and l₂  respectively, As the Galvanometer reads zero, points B and D are at the same potential .This means that voltage drops from A to B and A to D must be equal. Also voltage drops from B to  C and D to C must be equal.Hence .

 For balanced bridge the potential drop across AB= the potential drop across AD

                        I₁P=I₂R

similarly the potential drop across BC= the potential drop across DC.

And                  I₁Q=I₂X                                                              

By dividing both the above equations we will get

                  P/Q=R/X

                PX=RQ

 Hence   X=RQ/P

If the three resistance on the right side of the above equation are known then the fourth resistance X can be calculated. Therefore by using Wheatstone bridge we can find the unknown resistance if we know other resistance.

Example of Wheatstone Bridge

The unbalance Wheatstone bridge is given in figure .Calculate the output voltage across points C and D and the value of resistor R₄ required to balance the bridge circuit.

For the first arm ACB,

For the second series arm ADB

The voltage across points C-D is,

The value of resistor, R₄ required to balance the bridge is ,

According to the above equation that the Wheatstone bridge have two input terminal (A ,B)and two output terminal(C,D).When the bridge is balance then the voltage across the output terminal is zero. When the bridge is unbalanced then the output voltage may either be positive or negative which depend upon the direction of balance

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