Kalvin Double Bridge

A Kelvin bridge (also called a Kelvin double bridge and in some countries a Thomson

bridge) is a measuring instrument invented by

William Thomson, 1st Baron Kelvin. It is used to measure an

unknown electrical resistance below 1 Ω.Its operation is similar to the

Wheatstone bridge except for the presence of additional resistors

These additional low value resistors and the internal configuration of the bridge are arranged to substantially

reduce measurement errors introduced by voltage drops in the high current (low resistance) arm of the bridge

It consist of two ratio arms. The outer ratio arm contains the known resistors and the inner ratio arm helps to connect the one terminal of the galvanometer at the appropriate point (which was the disadvantage of the Kelvin first bridge).

The set of ( Ra , Rb ) ratio arms eliminate the

effect of the resistance Ry by having :

LMPKL

PK

EE

EE

Now , the (G) will indicate a zero current i.e BALANCEDWhen:

2

1

R

R

R

R

b

a 1

2

Now using voltage division V.D:

similar:

ERR

REKL

12

2

MPLMLMP EEE

RIE (In

general )

yba

yba

RRR

RRRRRI

)(( 43

1`

2`

; From these we will have the equation balanced

).

( 3yba

yblmp RRR

RRRIE

lmpkl EE

;Equation of balance 32

14 .RR

RR

As said earlier , the kelvin bridge is used to

measure very low resistances

(as low as 0.0001 Ω)

AC – BRIDGE

Here , the balance conditions is reached

when the detector response is zero

to obtain a balance in the bridge , One or more

arms may be adjusted.

Which leads to

)()(42

231

1

2211

ZZ

EZ

ZZ

EZ

ZIZI

EE BCBA

3241 ZZZZ

32324141 ZZZZ33224411 .. ZZZZ

3241 .. ZZZZ 3241

Ex : given an AC bridge with

Solution:

30400

250

80100

3

2

1

Z

Z

Z

3241 .. ZZZZ 10004Z

3241 504

MAXWELL BRIDGE

Measures inductance in terms of a known capacitance

here ; 3241 .. ZZZZ

132

1324

..

1.

YZZ

ZZZZ

]1

[ 11

324 jwCR

ZZZ

Note that: 1

111

11jwC

RZY

12

3

3211

324 RRjwC

R

RRZ

44 jwLR

4

5

Notes: 1.The measurment of the

Maxwell is for medium-Q coil ((1<Q<10 )

2 .Balancing the maxwell bridge is by:

a.Adjusting R3 for inductive balance

b.Adjusting R1 for resistance balance

c.Repetation of 1 & 2 until a compelete balance is obtained

HAY Bridge

Note :this bridge is used for measuring

high Q coils

3241 ZZZZ

1321

1

ZZZZ

Where

jwCRZ

111

444 jwLRZ

xxx jwLRZ 4RRx 4LLx 4ZZ x

Which leads

321 ))(( RRjwLRwC

jR xx

3211

1 RRRjwLwC

jR

C

LRR x

Xxx

321

1 RRC

LRR xx

1RjwLwC

jRx

X

Solving for Rx & Lx

21

21

2132

1 RCw

CRRLx

21

21

2321

21

2

1 RCw

RRRCwRx

L

C

xR

1R

xjwL

1

1

wCj

Notice that :the inductive phase angle is

equal to the capacitive phase angle

Inductive phase capacitive phase

we have

hence ;

then ;

QR

wL

x

xL tan Q

RwC xC

1

1tan

QCL tantan

x

xL R

wLQ

11

1

RwCQC

211

2 )()1

( RwCQC

21

21

2132

1 RCw

CRRLx

2

132

11Q

CRRLx

notice here that for :

Q >10

2

132

101

1

CRRLx

01.01132

CRRLx

132 CRRLx

Notice that if 0<Q<10 ( meduim –Q coil )

measurment base on the maxwell bridge is used even

though for Q>10

which is similar to the max for Q >10

then HAY bridge is more accurate .

132CRRL

x

Detection in the AC bridges :

here , the balance condition is measured when the response in

the detector is zero Using a pair of head phones sets that completely surrounding the ears (closed –cup-type) One can detect currents of less than 0.1 µA .

Listening to the headphones , as the R3 is adjusted , a condition of balance will be realized when the headphones fail to produce (clicks ) as the switch is actuated

Done By :Wala’ Al.Nsour