What is the theory of kelvin's double bridge experiment?

Answer 1

Theory: -

Kelvin's bridge is a modification of whetstone's bridge and always used in

measurement of low resistance. It uses two sets of ratio arms and the four terminal

resistances for the low resistance consider the ckt. As shown in fig. The first set of ratio P

and Q. The second set of ratio arms are p and q is used to connected to galvanometer to a

pt d at an Approx. potential between points m and n to eliminate the effects of connecting

lead of resistance r between the known std. resistance 's' and unknown resistance R

.The ratio P/Q is made equal to p/q. under balanced condition there is no current flowing

through galvanometer which means voltage drop between a and b, Eab equal to the

voltage drop between a and c, Eamd.

Now

Ead=P/P+Q ; Eab=I[R+S+[(p+q)r/p+q+r]] ------------(1)

Eamd= I[R+ p/p+q[ (p+q)r/p+q+r]] ---------------------(2)

For zero deflection->Eac=Ead

[ P/P+Q]I[R+S+{(p+q)r/p+q+r}]=I[R+pr/p+q+r] ----(3)

Now, if

P/Q=p/q

Then equation… (3) becomes

R=P/Q=S ------------------------------------------------------(4)

Equation (4) is the usual working equation. For the Kelvin's Double Bridge .It indicates

the resistance of connecting lead r. It has no effect on measurement provided that the two

sets of ratio arms have equal ratios. Equation (3) is useful however as it shows the error

that is introduced in case the ratios are not exactly equal. It indicates that it is desirable to

keep r as small as possible in order to minimize the error in case there is a diff. between

the ratio P/Q and p/q.

R=P/QS

Answer 2

Kelvin's double bridge experiment is a method used to measure low resistances accurately. It combines the principle of Wheatstone bridge with Kelvin's methodology to nullify the effects of lead resistance. By using two ratio arms and a ratio set, this setup allows for highly precise measurements of resistance.