Wheatstone Bridge

A resistance can be measured by Ohm’s law using a voltmeter and an ammeter in an electrical circuit. But this measurement may not be accurate for low resistances. To overcome this difficulty, a wheatstone bridge is used. It is an arrangement of four resistances which can be used to measure one of them in terms of the other three.

P and Q are two adjustable resistances connected in arms AB and BC. R is an adjustable known resistance. S is an unknown resistance to be measured. A sensitive galvanometer G along with a key K₂ is connected in the arm BD. A battery E along with a key K₁ is connected in the arm AC.

On closing the keys, in general, some current will flow through the galvanometer and you can see a deflection in the galvanometer. It indicates that there is some potential difference between points B and D.

Point B is at a higher potential than point D

Current will flow from B towards D and the galvanometer will show a deflection in one direction, say right.

Point B is at a lower potential than point D

Current will flow from point D towards B and the galvanometer will show a deflection in the opposite direction.

Both points B and D are at the same potential

In this case, no current will flow through the galvanometer and it will show no deflection, i.e. the galvanometer is in null condition. In this condition, the Wheatstone bridge is said to be in the state of balance.

The points B and D will be at the same potential only when the potential drop across P is equal to that across R.

I₁P = I₃R

I₁ = I₂ + I_G

I₄ = I₃ + I_G

Applying Kirchhoff’s first rule at junctions B and D in the null condition (I_G = 0),

I₁ = I₂

I₃ = I₄

Also potential drop across Q will be equal to that across S. Hence,

I₂Q = I₄S

P/Q = R/S

This is the condition for which a Wheatstone bridge will be balanced.

S = QR/P

The main factor affecting the accuracy of measurement by Wheatstone bridge is its sensitivity with which the changes in the null condition can be detected. It has been found that the bridge has the greatest sensitivity when the resistances in all the arms are nearly equal.