The Wheatstone bridge is a device used to measure unknown electrical resistance. It consists of four resistors arranged in a diamond shape with two resistors of known value, one resistor of unknown value, and one variable resistor. By adjusting the variable resistor to balance the bridge circuit and produce a null reading on the galvanometer, the ratio of the two legs is equal to the ratio of the unknown resistor to the variable resistor, allowing the unknown value to be determined. The Wheatstone bridge works on the principle of null deflection and accurate resistance measurement.

1. Wheatstone Bridge:--The device uses for
the measurement of minimum resistance with the help of
comparison method is known as the Wheatstone bridge.
Wheatstone bridge, also known as the resistance bridge.
Used to calculate the unknown resistance by balancing two legs
of the bridge circuit.
It was invented by Samuel Hunter Christie in the year 1833, which was
later popularized by Sir Charles Wheatstone in 1843.
This bridge is very reliable as it gives accurate measurements.
A Wheatstone bridge consists of two I / p and two o / p terminals
includes of four resistors arranged in a diamond shape.
Wheatstone Bridge:--

2. principle :-- The Wheatstone
bridge works on the principle of
null deflection, i.e. the ratio of
their resistances are equal and no
current flows through the circuit.
The bridge is said to be in a
balanced condition when no
current flows through the
galvanometer.

3. Construction of Wheatstone Bridge
Ratio arms AB and BC :--A Wheatstone bridge circuit consists of four arms of
which two arms consists of known resistances.
One unknown resistance :-- One arms consist of an unknown resistance.
Standard arm :-- One arms consist of a variable resistance.
Galvanometer :-- The circuit also consists of a galvanometer .The current
that flows through the galvanometer depends on the potential difference
across it.
An electromotive force source:-- The emf source is attached between
point A and C while the galvanometer is connected between the
points B and D.
K K :---Keys used to complete circuit. K is attached between point A and C. K
is connected be tween the points B and D.

4. Wheatstone Bridge and Its Working
A Wheatstone bridge is widely used to measure the electrical
resistance . When key K is pressed current I is provided by the cell.
At point A current is divided into two parts one part I want passes
through resistance P while other part I goes through resistance R .Now
resistances P, Q , R and S are also adjusted that on pressing the key K
there is no deflection in the Galvanometer G, it means there is no
current in the diagonal BD .Thus same current will pass through
resistance Q which is in resistance P and same current
I will pass through S which is in resistance R.

5. Currents through the arms are assumed by applying
Kirchhoff’s Junction Rule.
Applying Kirchhoff’s Loop Rule for :
Loop ABDA:
-I1.P - Ig. G + (I - I1).R = 0
Loop BCDB:
- (I1 - Ig).Q + (I - I1 + Ig).S + Ig. G = 0
When Ig = 0, the bridge is said to balanced.
-I1.P + (I - I1).R = 0
- (I1 ).Q + (I - I1 ).S = 0
P Q
=
R S
I1
I
Ig I1 - Ig
I - I1
I
II
I - I1 + Ig
E
A
B
C
D
P Q
R S
G

6. Note
In balance condition potential at point B and D will be same so to find the
equivalent resistance between A and C, the resistance connected between B
and the can be neglected because no current flows through it.
In balance condition if position of galvanometer and cell are interchanged
then there will be no effect on the balancing state of the bridge. So the
diagonal arms AC and BD of bridge are said to be conjugate arms.
Greater is the deflection in Galvanometer with small deviation in balanced
state of the bridge, greater is said to be sensitivity of the bridge. Bridge is
maximum sensitive when resistance P Q R and S are the same order.