What is Wheatstonc hridge ? Explain its principle.

Explanation

`rArr` Wheatstone bridge is special network of four resistors and battery connected as shown in figure below.

`rArr` Four resistors `R_(1) , R_(2) , R_(3) and R_(4)` are connected with battery as shown in figure.
`rArr` Battery is connected between A and C called battery arm.
`rArr` Galvanometer is connected between B and D hence, it is called galvanometer arm. `rArr` Consider battery is to be ideal (zero internal resistance).
`rArr` Current flowing in resistor `R_(1), R_(2), R_(3) and R_(4)` be `I_(1), I_(2), I_(3) and I_(4)` respectively.
`rArr` Current will be flowing through all four resistors and galvanometer.
In special condition when current through galvanometer is zero (lg = 0) Wheatstone bridge is said to be in balanced condition.
`rArr` In balanced condition of Wheatstone bridge
`I_(1) = I_(3) and I_(2) = I_(4)` .
`rArr` By using Kirchhoff.s second law for loop ABDA.
`-I_(1) R_(1) + 0 + I_(2) R_(2) = 0 " " [ because I_(g) = 0 ] `
`therefore I_(1) R_(1) = I_(2) R_(2) " " `... (1)
Similarly for loop BCDB,
`I_(4) R_(4) + 0 - I_(3) R_(3) = 0`
by substituting `I_(3) = I_(1) and I_(4) = I_(2)`
`I_(2) R_(4) - I_(1) R_(3) = 0`
`therefore I_(1) R_(3) = I_(2) R_(4) " "` ... (2)
Comparing equation (1) and (2) ,
`(R_(1))/(R_(3)) = (R_(2))/(R_(4))`
`therefore (R_(1))/(R_(2)) = (R_(3))/(R_(4)) " or " (R_(2))/(R_(1)) = (R_(4))/(R_(3))`
`rArr` This equation represent principle of Wheatstone bridge which is condition for balance of Wheatstone bridge.
`rArr` As an application of Wheatstone bridge value of `R_(1), R_(2), R_(3)` are known and `R_(4)` is unknown then, `R_(4) = R_(3) xx (R_(2))/(R_(1))` will give value of unknown resistor `R_(4)`.