Wheatstone's Bridge(Measurement Of Resistance)

 A bridge in its simplest form consists of a network of 4 resistance arms forming a loop , with a dc source of current applied to 2 opposite junctions and a current detector connected to the opposite two junctions.

Bridge circuits are extensively used for measuring components values like R, L and C. Since the bridge merely compares the worth of an unknown component thereupon of an accurately known component (a standard), its measurement accuracy are often very high. This is because the readout of this comparison is predicated on the null indication at bridge balance, and is actually independent of the characteristics of the null detector. The measurement accuracy is therefore directly related to the null indicator used. The basic dc bridge is used for accuracy measurement of resistance and is called whetstone’s bridge.
Whetstone’s bridge is the most accurate method available for measuring resistances, ranging from approximately one ohm to several mega ohms.
Figure shows the circuit diagram of a whetstones bridge.

 Wheatstone's Bridge

The source of emf and switch is connected to points A and B.
A sensitive current indicating meter, the galvanometer, is connected to points C and D.
The galvanometer is a sensitive micro ammeter, with a zero centre scale when there is no current through the meter, the galvanometer pointer resets at O. i.e mid scale
Current in one direction causes the pointer to deflect on one side and current within the other way to the opposite side.
When SW₁ is closed, current flows and divides into the two arms, at the pointer A, i.e I₁ and I₂.
The bridge is balanced when there is no current through the galvanometer, (or) when the electrical potential at point C and D is equal i.e the potential across the galvanometer is zero.
To obtain the bridge balance equation, we have form the figure.

I₁R₁ = I₂R₂                   ........................             (1)

For the galvanometer current to be zero, the following conditions should be satisfied.

I₁ = I₃ = E / R₁ + R₃        ........................           (2)

I₂ = I₄ = E / R₂ + R₄        ........................           (3)    

Combing equations (1),(2) and (3) and simplifying, we obtain

E / R₁ + R₃ = E / R₂ + R₄

R₁ *( R₂ + R₄)  = (R₁ + R₃) * R₂

R₁R₂ + R₁R₄ = R₁R₂ + R₃R₂

R₄ = R₂R₃ / R₁ ( or)  R₁R₄ = R₂R₄    .............    (4)

This is the equation for the bridge to be balanced. If three of the resistances have known values, the fourth may be determined form eq(4). Hence , if R₄ is the unknown resistor , its resistance Rx can be expressed in terms of the remaining resistor, as follows.
R_x = R₃ . R₃ / R₁
Resistor R₃ is named the “Standard arm” of the bridge, and resistor R₂ and R₁ are called the “Ratio arms”.
The measurement of unknown resistance R_x is independent of the characteristics or the calibration of the null detaching galvanometer, provided that the null detector has sufficient sensitivity to indicate the position of the bridge with the specified degree of precision.
APPLICATIONS:
A wheatstone bridge may be used to measure the dc resistance of various of wire either for the purpose of quantity control of the wire itself, or f some assembly in which it is used. For example, the resistance of motor windings, transformers, solenoids, and relay coils are often measured.
It is also used extensively by telephone companies and others to locate cable faults. The fault could also be two lines shorted together, or one line shorted to ground.
LIMITATIONS:
For low resistance measurement, the resistance of the leads and contacts becomes significant and introduces a error. This can be eliminated by Kelvin’s double bridge.
For high resistance measurements, the resistance presented by the bridge becomes so large that the galvanometer is insensitive to imbalance. Hence a power supply has to replace the battery and a dc VTVM replaces the galvanometer.
In the case of high resistance measurements in mega ohms. The wheatstones bridge cannot be used.
The rise in temperature causes a change within the value of the resistance, and excessive current may cause a permanent change in value.