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 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).

Now , the (G) will indicate a zero current i.e BALANCED When : The set of ( Ra , Rb ) ratio arms eliminate the effect of the resistance Ry by having : Now , the (G) will indicate a zero current i.e BALANCED When : 1 2

Now using voltage division V.D: similar : 1` 2` (In general)

;From these we will have the equation balanced ;Equation of balance

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

Ex : given an AC bridge with Solution :

MAXWELL BRIDGE

Measures inductance in terms of a known capacitance here ; Note that : 1 2 3 4 5

1.The measurment of the Maxwell is for medium-Q coil ((1<Q<10 ) 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 Where

Which leads

Solving for Rx & Lx

capacitive phase Inductive phase Notice that : the inductive phase angle is equal to the capacitive phase angle

we have hence ; then ;

notice here that for : Q >10

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 .

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