# Wheatstone Bridge Formula

## Wheatstone Bridge Formula

Scientists employ a variety of techniques to study the world around them. They use their senses to observe things and collect data. Some observations are straightforward, while others are more complicated. Thus, measurements may be necessary if researchers want to learn more about the substance. In science, measurement is a crucial component. Without the ability to measure, conducting experiments using only theories is challenging. One such crucial instrument for experimentation and measurement is the Wheatstone Bridge. The use of it in electrical circuits is widespread. The Wheatstone Bridge Formula is used by scientists and engineers, and it is also important for students to learn.

Students are introduced to the Wheatstone Bridge Formula in school, and they are under immense pressure to get the formula right. The application of the Wheatstone Bridge Formula is another challenge for the students.

## Wheatstone Bridge Formula

It is a crucial instance of Kirchhoff’s rules being applied in physics. Resistance comparisons and the identification of unidentified resistances in electrical circuit networks are both applicable. The Resistance Bridge is another name for Wheatstone Bridge in the Wheatstone Bridge Formula.

By balancing the two bridge circuit legs, one of which contains the component of unknown resistance, it is possible to calculate the unknown resistance. In the year 1833, Samuel Hunter Christie created it. Sir Charles Wheatstone later made it popular in 1843, and it became famous as the Wheatstone Bridge Formula.

### What is the Wheatstone bridge?

This bridge is made up of four resistances, P, Q, R, and S, that are connected along the four sides of a square-shaped circuit (let’s say ABCD). Additionally, it has a galvanometer G connected to it between the points B and D. The galvanometer has a resistance of G and a current flow of IG.

As a result, the circuit is made up of a bridge-shaped connection between two known resistors, one unknown resistor, and one variable resistor. Because it provides precise measurements, this device is extremely dependable. Students should learn the Wheatstone Bridge Formula to understand all of these aspects of the formula.

### Wheatstone Bridge Principle

It operates on the null deflection principle, which states that no current flows through the circuit because the ratio of their resistances is equal. The bridge will typically be in an unbalanced state where current flows through the galvanometer.

When the galvanometer has no current flowing through it, the bridge will be balanced. By adjusting the known resistance and variable resistance, one can achieve this condition. This is an important aspect of the Wheatstone Bridge Formula. Students can learn all about the Wheatstone Bridge Formula from the Extramarks platform.

The Wheatstone Bridge Formula can be learned in an interactive manner with the help of the Extramarks platform. The platform comes with multiple explanations for the formula that make learning accessible for students. Accessibility of learning brings in interactive study modules and videos for students to understand the concept. Students can also prepare the Wheatstone Bridge Formula for examinations with the help of the sample papers and previous year papers on the Extramarks app.

The formula for Wheatstone bridge

Following is the formula for Wheatstone bridge:

R=PSQ

Where,

R The unknown resistance

S Standard side of the bridge

P and Q The ratio of the sides of the bridge

Solved Examples

Q.1: In a Wheatstone’s bridge P = 100 Ω,Q=1000ΩandR=40Ω. If its galvanometer shows the zero deflection, then determine the value of resistance S.

Solution:

We have the known resistances as:

P = 100 Ω,

Q = 1000 Ω and

R = 40 Ω

For zero deflection in galvanometer, we have whetstone bridge formula as:

PQ = RS

i.e. S = QP×R

i.e. S = 1000100×40

S = 400Ω.

Q. 2: What will be the value of ‘r’ when the Wheatstone’s network is in balanced condition? Following values are known:

P = 500Ω,Q=800Ω,R=(r+400)Ω,S=1000Ω.

Solution: Given parameters are:

P = 500Ω,Q=800Ω,R=(r+400)Ω,S=1000Ω.

For balanced condition the bridge, we have whetstone bridge formula as:

PQ = RS

i.e. 500800=r+4001000

i.e. r + 400 = 58×1000

r = 625 -400 = 225 Ω