The Kelvin double bridge is one of the best devices available for the precise measurement of low resistances. It is the modification of wheatstone bridge by which the errors due to contact resistance and lead resistances are eliminated. This bridge is named double bridge because it contains a second set of ratio arms. An interesting variation of the Wheatstone bridge is the Kelvin Double bridge, used for measuring very low resistances (typically less than 1/10 of an ohm)

Consider the bridge circuit shown in figure below. Here ‘r’ represents the resistance of the lead that connects the unknown resistance ‘R’ to standard resistance ‘S’. Two galvanometer connections indicated by dotted lines are possible. The connection may be either to point 'm' or to point 'n'. When the galvanometer is connected to point ‘m’ the resistance ‘ r’ of the connecting leads is added to the standard resistance ‘S’ resulting in indication of too low an indication for unknown resistance ‘R’. When the connection made to point the resistance ‘r’ is added to the unknown resistance resulting in indication of too high a value for ‘R’.

Suppose that instead of using point ‘m’ which gives a low result or ‘n’ which makes the result High, we make the galvanometer connection to any intermediate point‘d’ as shown by full line. If at point‘d’ the resistance ‘r’ is divided into two parts r1, r2 such that

**r1/r2 = P/Q**

Then the presence of r the resistance of connecting leads causes no error in the result. We have,1

Therefore we conclude that making the galvanometer connection as at C, the resistance of leads does not effect the result.

The process described above is obviously not a practical way of achieving the desired result, as there would certainly be a trouble in determining the correct point for galvanometer connection. It does however suggest the simple modification that two actual resistance units of correct ratio be connected between points ‘m’ and ‘n’ the galvanometer be connected to the junction of the resistors. This is the actual Kelvin bridge arrangement which is shown in figure below.

The Kelvin double bridge incorporates the idea of a second set of ratio arms, hence the name of double bridge- and the use of four terminal resistors for the low resistance arms. Figure shows the schematic diagram of the Kelvin Bridge. The first of ratio arms is P and Q. The second set of ratio arms, p and q is used to connect the galvanometer to a point ‘d’ at the appropriate potential between points ‘m’ and ‘n’ to eliminate the effect of connecting lead of resistance ‘r’ between the known resistance ‘R’ and the standard resistance ‘S’.

The ratio p /q is made equal to P/Q. Under balance conditions there is no current through the galvanometer, which means that the voltage drop between a and b, E is equal to the voltage drop Ed between a and b.

Now if p/q = p/q becomes R = P / Q *S

Above equation is the usual working equation for the Kelvin double bridge. It indicates that the resistance of connecting lead ‘r’ has no effect on the measurement provided that the two sets of ratio arms have equal ratios. The above equation is useful however as it shows the error that is introduced in case the ratios are not exactly equal. It is indicated that it is desirable to keep ‘r’ as small as possible in order to minimize the errors in case there is a difference between ratios P / Q and p/q.

In a typical Kelvin bridge, the range of resistance calculated is 0.1S to 1.0S.

As it can be seen from the front panel diagram of the unit, the range selection on the arms Q, q have been changed so that the user can have the option of balancing the bridge to the exact ratio of.

**P/Q = p/q**

This provides an additional plus point to the user while selecting the range of output and thus enabling him to obtain the exact balance point.

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