Question

Derive an expression for wheatstWhe bridge

Answer 1

Wheat Stone Bridge

Wheat stone is an arrangement used to find the value of unknown resistance.

Construction

It consist of four resistance P,Q,R,S arranged in such a way that they form a quadrilateral ABCD in which P and Q are known as constant resistance,R is known variable resistance and S is unknown resistance.Voltage is appled across AC while a Galvanometer and key is connected across BD.

on pressing the key 'K' if there is no deflection in the galvanometer,then the Bridge is said to be balanced and in balanced condition P/Q=R/S which is possible only when B and D are at same potential.

PROOF

let VA,VB,VC and VD are the potential of A,B,C and D respectively.

let I1 , I2 be the current given to the circuit and Ig be the current flow across BD.

Now Across AB

VA-VB=I1 P --------(1)

Across BC

VB-VC=(I1-Ig)Q -----(2)

Across AD

VA-VD=I2R --------(3)

Across DC

VD-VC=( I2 + Ig)S ---------(4)

at Balanced Condition

B and D are having same potential

i.e, VB=VD

and Ig=0

therefore equation changes to

VA-VD=I1 P ------(5)

VD-VC=I1 Q ------(6)

VA-VD=I2 R ------(7)

VD-VC=I2 S ------(8)

I1 P=I2 R ------(9)

I1 Q=I2 S ------(10)

(9) / (10)

P/Q=R/S